You have good instincts with most of these picks, but the team could afford some fine-tuning to better hold its own. Where possible, I tried to preserve your original ideas for the team.
Ferrothorn
Speed EVs are irrelevant on Ferro and you shouldn't usually have both Spikes and Stealth Rock. Toxic and Iron Head, similarly, are usually worse than Leech Seed and Power Whip; the former helps with Ferro's longevity and the latter prevents Pokemon like Ting-Lu from getting too comfortable.

Ferrothorn @ Leftovers
Ability: Iron Barbs
Shiny: Yes
Tera Type: Steel
EVs: 252 HP / 80 Def / 176 SpD
Impish Nature
- Stealth Rock
- Leech Seed
- Knock Off
- Power Whip
This set also replaces Rocky Helmet with Leftovers. Rocky Helmet rewards aggressive play, which you don't need on this Ferrothorn — it also has a higher skill floor, so I recommend using the more common and more useful Leftovers instead. I also use Knock Off here instead of Spikes, because pressuring Boots Pokemon like Zapdos and Tornadus-Therian is more relevant in most cases.
Pelipper
Generally, slow U-turns are better than fast ones. This is because it allows you to bring in your Pokemon after the opponent has already made a move, keeping them healthy and more threatening over the course of the match. With that in mind...

Pelipper @ Damp Rock
Ability: Drizzle
Shiny: Yes
Tera Type: Water
EVs: 248 HP / 8 SpA / 252 SpD
Sassy Nature
IVs: 0 Spe
- Scald
- Hurricane
- U-turn
- Roost
This minimum Speed Pelipper underspeeds other weather setters to make your rain more consistent, and it also provides the slowest possible U-turn into your sweepers. You'll see later I get rid of your team's hazard removal — you can slot Defog over Hurricane on Pelipper if it matters to you, but I would play with the team first and see if you're really that bothered by hazards.
Swampert-Mega
This is a great choice for a rain team, but there are still a few tweaks to make it better.

Swampert-Mega @ Swampertite
Ability: Swift Swim
Shiny: Yes
Tera Type: Water
EVs: 252 Atk / 4 SpD / 252 Spe
Jolly Nature
- Liquidation
- Earthquake
- Ice Punch
- Flip Turn
I'm not sure what your EV spread is doing and in most cases it's better to go max Attack and max Speed. Waterfall has been swapped with Liquidation for the power boost — the latter's 5 extra BP may seem insignificant, but it will be more relevant than Waterfall's 20% flinch chance. I also replaced Bulk Up with Flip Turn because it lets Swampert get the jump on its resists (e.g. Alomomola) and bring in a more relevant teammate.
Tapu Koko
You were correct that an Electric type is a good fit for this team... just not this Electric type. :P
Raging Bolt is pretty much mandatory on rain teams because it erases bulky Water types and has more longevity than other options.

Raging Bolt @ Dragonium Z
Ability: Protosynthesis
Tera Type: Electric
EVs: 252 SpA / 4 SpD / 252 Spe
Modest Nature
IVs: 20 Atk
- Weather Ball
- Thunderbolt
- Draco Meteor
- Thunderclap
Raging Bolt is fairly customizable, so feel free to play around with any of this barring the mandatory Thunderclap. I opted for Thunderbolt over Thunder because I wouldn't expect the rain to be up all the time and it is valuable to have a consistent STAB option; it also has more PP, which is relevant against Corviknight. Draco Meteor + Dragonium Z gives Raging Bolt a nuclear STAB option that breaks down bulky Pokemon (particularly Ground types that would otherwise wall this set when the rain isn't up). Weather Ball synergizes nicely with rain and threatens the aforementioned bulky Ground types more easily.
Again, there are a few other options you can play around with. Dragon Pulse is more consistent Dragon STAB, Thunder is an option in rain, Calm Mind makes Raging Bolt stronger into Pokemon like Slowking-Galar, and Leftovers makes it easier to consistently set up. If my set doesn't work for you, try some of these options instead.
Kartana
I'm really not a fan of totally gutting your original team, but Kartana sticks out like a sore thumb here. It is not particularly relevant on rain and seems to only serve the purpose of threatening opposing Ferrothorn. Knowing this, I recommend:

Urshifu-Rapid-Strike @ Choice Band
Ability: Unseen Fist
Tera Type: Fighting
EVs: 252 Atk / 4 Def / 252 Spe
Jolly Nature
- Surging Strikes
- Close Combat
- U-turn
- Ice Spinner
Urshifu-Rapid-Strike is a much better fit on rain teams and pressures Ferrothorn with Close Combat. The Choice Band and strong moves make it a powerful wallbreaker — Surging Strikes is especially helpful against Gliscor and Landorus-Therian. Ice Spinner is an option against Latios-Mega and other Dragon types, with U-turn serving to pressure defensive Pokemon like Toxapex that Urshifu cannot break. You can also use a Choice Scarf here, but I opted for the Band for stronger breaking power and because Swampert-Mega in rain fills the role of "really fast Water type" already.
Breloom
It breaks my heart, but unfortunately Breloom just isn't very good in National Dex. For your final slot, you want an aggressive Pokemon that covers your existing weaknesses, which Breloom just... doesn't do. My recommendation is Weavile, which helps answer Ogerpon-Wellspring, Gholdengo, Slowking-Galar, and Gliscor.

Weavile @ Heavy-Duty Boots
Ability: Pressure
Tera Type: Dark
EVs: 252 Atk / 4 SpD / 252 Spe
Jolly Nature
- Triple Axel
- Knock Off
- Swords Dance
- Ice Shard
Choice Band is more common on Weavile, but I think Heavy-Duty Boots + Swords Dance works better here because you already have a Banded Pokemon in Urshifu. With Boots, Weavile can safely come in on its positive matchups and clear the field for its teammates. Ice Shard is notably your team's fastest priority option and provides insurance against opposing Raging Bolt's Thunderclap.
Weavile isn't particularly common on rain teams, so you can also try more common options like Barraskewda, Archaludon, or Tornadus-Therian. I just think Weavile nicely ties your team together as a strong, fast priority user that threatens Pokemon like Gholdengo, which you otherwise doesn't appreciate.
And that's the team! I didn't intend to gut half your picks going into this, but hopefully my suggestions help you. Good luck and enjoy!
Pokepaste here