In your Linoone's case, it very likely has the Ability Pickup. Here's what Bulbapedia says:
At the end of the turn in which another Pokémon used a one-time use item (including throwing an item with Fling or using Natural Gift), a Pokémon with Pickup will collect the item if they are not holding anything. If more than one Pokémon has Pickup or Harvest, the faster Pokémon will restore an item first. If multiple items can be collected, the Pokémon will collect the item most recently consumed.
Pickup is a useful Ability in-game because it can allow you to get a variety of hard-to-get items, like Rare Candies and even Leftovers. Check my source above for a complete list of every item possible.
Not all items are useful to be held, however. Some are completely useless (e.g. Rare Candies) as held items, but function well in different ways. There are some notable items and item classes that are good hold item choices.
- Berries can sometimes mean the difference between winning and losing a battle. Oran Berries are good in the early game, when your Pokemon don't have as much HP. Sitrus Berries are solid items for the whole game, as they restore 25% of a Pokemon's HP. Other berries, like Pecha, Rawst, and Aspear, can cure status conditions of your Pokemon (poison, burns, and freeze respectively). Still other berries, like the Salac Berry, give your Pokemon a boost to their stat in a pinch (the Salac Berry boosts Speed of a Pokemon holding it at 25% or less HP). A word of warning -- berries can only be used once each.
- Choice items provide a boost to one of your stats in exchange for your Pokemon only being able to select one move. The Choice Band boosts Attack, the Choice Scarf boosts Speed, and Choice Specs boost Special Attack. All are useful, and can mean the difference between you fainting or your opponent fainting. They are non-consumable, and the move you can choose resets upon switching out. Make sure not to give a Pokemon a useless one, however (for example, giving a Weavile Choice Specs or a Wobbuffet Choice Scarf).
- The Eviolite is tremendously useful for NFE (not fully evolved) Pokemon, but useless for those that cannot evolve any further. It boosts both Defense and Special Defense of a Pokemon that can still evolve: for instance, Type: Null and Galarian Corsola. It does not work on Pokemon that are standalone lines: for example, Unown and Komala. This item can mean the difference between an OHKO and a 2HKO, a 2HKO and a 3HKO, and so on. Extra staying power is always a good thing, and this item can make some Pokemon slightly viable.
- The Life Orb can be considered an alternative to the Choice Band and Choice Specs. It boosts your damage output, in exchange for your Pokemon losing a bit of its health each turn. It's good for suicide attackers that you don't expect to last (Darmanitan-U is a prime example), or Pokemon that simply need the extra power boost. The advantage of using a Life Orb over the Choice items is that it does not limit you to using just one move.
- Assault Vest boosts your Pokemon's Special Defense, at the cost of it only beinng able to select attacking moves. It's not very good on Pokemon that already have high Special Defense, or those that need non-attacking moves to be good. It can be a nice item on Pokemon like Excadrill and Cinderace, which have low Special Defense and enough raw power to not need setup moves.
- Focus Sashes are tremendously good. They allow frail Pokemon to live one more hit than they usually would be able to, or set up a free boosting move, like Swords Dance or Agility. They only work at full health, which shouldn't be an issue for frail Pokemon that would have been OHKOed anyways. Note that Focus Bands are not as good, as they are far too gimmicky to be reliable.
- Leftovers provide your Pokemon with a small amount of their HP back at the end of every turn. They're good for bulky Pokemon like Blissey and Registeel, where that small bit of health recovery can mean the difference between a KO that turn and a KO the next turn. They aren't too good on frail Pokemon like Pheromosa, as that sort is more likely to be OHKOed or 2HKOed anyways.
- The White Herb is useful on a great many Pokemon. It resets any negative stat changes the user receives, but it can only be used once. Pokemon like Hawlucha and the Hitmons use them well, as with this item, they can use Close Combat once with zero downsides. Pokemon that utilize Shell Smash (most commonly Polteageist, Cloyster, Blastoise, and Crustle) use White Herb in order to reset the Defense and Special Defense drop that comes from using Shell Smash, allowing them to sweep more effectively.
- Light Clay is just amazing. It allows Pokemon like Klefki, Grimmsnarl, Vanilluxe, Alolan Ninetales, and other leads to set up Light Screen, Reflect, and Aurora Veil, and have them last more time than they usually do (eight turns in comparison to the usual five). It's an invaluable item to Pokemon like this, and a Pokemon with a screen move should probably be holding it.
- Heavy-Duty Boots are one of the best items added in Generation 8. They're tremendously helpful on Pokemon like Vanilluxe, Charizard, Volcarona and Cinderace, for their use in completely blocking all entry hazard damage. Charizard and Volcarona use them to protect from Stealth Rock, as they would ordinarily take 50% of their health without Heavy-Duty Boots. The item can also be good on Rapid Spinners and Defoggers, so they aren't worn down by clearing hazards. Many Fire, Ice, and Bug types use this if there's no other item that's better (Light Clay for Vanilluxe, sometimes Life Orb for Weavile, etc.).
There are a few other items that aren't as good as the ones I mentioned, but can still serve a use on the right Pokemon.
- Scope Lens is a bit unreliable, but it's good when put on a Pokemon with Sniper, like Kingdra or Inteleon, as you can score guaranteed critical hits.
- Wide Lens is fairly useless in comparison to other items, but the accuracy boost can prove helpful in some cases.
- Type-boosting items aren't very useful competitively, as things like Life Orb and the Choice items are better, but they work just fine in-game.
- The Expert Belt can be good on specific Pokemon competitively, but it's usually outclassed by things like Life Orb and the Choice items. Zeraora utilizes it effectively, however.
- Grassy / Psychic / Misty / Electric Seeds can be nice on things like the Tapus, Rillaboom, Alolan Raichu, and Hawlucha, but they usually require your team to be Terrain-based. If you don't want to accommodate a Terrain setter (the Tapus, Indeedee, Pincurchin, Galarian Weezing, and the Grookey line), the Seeds are practically deadweight.
- The Power Herb really only sees use on Xerneas, for its ability to set up Geomancy in one turn. It is sometimes used on Pokemon like Omastar for a one-turn Meteor Beam, but that's not too common. Most other Pokemon that could benefit (Solar Beam users mainly) are generally centered around a weather team or something else that shortens the amount of turns their move takes.
- The Rocky Helmet is a little situational, but it works. It can be good on Pokemon with Rough Skin or Iron Barbs (commonly Garchomp and Ferrothorn) so the damage a physical attacker takes is compounded. It also occasionally sees use on walls like Umbreon that can take a lot of hits.
- Berry Juice, while completely useless in most formats, can be good in LC. Sturdy users like Magnemite and Onix use them to go back to full health after setting up or posing a general annoyance, plus they get their Sturdy back. (Magnemite uses Recycle to do it multiple times, and Onix generally sets up a Dragon Dance or two)
There are also some items that may sound good as held items in theory, but in practice, they're not so good.
- Shell Bell may look pretty appealing -- HP restored every time you attack sounds pretty decent on paper. In practice, however, it's just an inferior Leftovers. Leftovers restores your health at the end of the turn no matter what, while Shell Bell only does so if you attack. The only reason to use Shell Bell is if you can't get enough Leftovers for your team (which isn't a problem in Showdown! anyways).
- Focus Bands are an interesting concept. A 10% chance to save you from being knocked out, however, just isn't good enough. There's no point on using Focus Band on a Pokemon that's usually going to get OHKOed (e.g. Pheromosa, Weavile, etc.), because 90% of the time, it'll do nothing. It could be useful on bulkier Pokemon, but Leftovers are almost always better in that case.
- Quick Claw has a similar problem to the Focus Band. A 20% chance to go first sounds good on paper, but 80% of the time, it's a waste of an item slot. You'd be better off with priority moves or something to boost damage output, like a Life Orb.
- Bright Powder and all the other items that raise your evasion are gimmicky and unreliable. The effect can be completely bypassed with moves like Knock Off, Aerial Ace, Swift, and others (though you don't see many Swift users in competitive). If you're playing a Smogon format, most of them ban accuracy changes anyways, so it's a complete waste in those cases.
- Muscle Bands and Wise Glasses both provide a 10% boost to a move of a specific category -- Muscle Bands for physical moves, Wise Glasses for special ones. This boost is almost nothing, however, and you would be better off with a Life Orb or Choice item.
- Safety Goggles aren't the greatest. Damage from sand and hail can be easily restored by Leftovers. Most Pokemon don't have powder moves worth using either. The best choice for this item would be Shedinja, as it dies to any weather damage, but Shedinja usually prefers a Focus Sash or Heavy-Duty Boots.
There were items that were good in previous generations, but not in Generation 8, usually because they're no longer in the game.
- Mega Stones were excellent in boosting a Pokemon's power to new levels, though only a few could use them. Prominent users like Mawile and Kangaskhan annihilated opponents in the era of Mega Evolution, making them almost a requirement for any team.
- Z-Crystals, while a mere one-time use per battle, were quite versatile. You could use them as a nuke to blast a hole in a wall or tank that you ordinarily would not be able to beat. They could also be used with the status moves to provide your Pokemon with a very helpful boost. One of the more notable uses of this was Z-Splash, which boosts the Pokemon's Attack stat by three stages.
- Type Gems, which were only around in the days of Generation 5 (except the Normal Gem, which has carried over to new generations, but no one uses that) were quite useful. They essentially served as a one-time type boosting item, which was excellent in cases. Holding a Flying Gem in conjunction with Acrobatics made for massive damage, as the Flying Gem's boost was taken into account, then consumed, then the no item boost was taken into account, meaning Acrobatics did a ton of damage the first time you used it. The other Gems weren't quite as useful, but they had their moments.
I've reached the character limit, but I'm not finished with this answer. The rest of it is on this Google Doc.
There are other items that are completely useless as held items, like your Linoone's mushrooms. These items can be sold, or in the case of things like evolution stones and Rare Candies, used for some other purpose.
Hope I helped!