As of Scarlet/Violet, Mew can learn Hydro Cannon, Frenzy Plant, and Blast Burn. These are the same games that removed Move Tutor moves, making them into TMs or, in the case of signature moves, relearnt via the Move Reminder.
The reason for this change is likely as a result of Mew not having as strong of a reputation of learning all Move Tutor moves, but it does for all TMs. As a result, it obtained the moves once they were available through TMs. Take a look at its Melee Trophy Data for instance. It would've been written after Move Tutor moves were introduced in Crystal, paying no mention to it.
Mew is an extremely rare Pokémon that has been seen by only a few people. Information on every Pokémon in the world is contained in Mew's cell structure, so it has the ability to use any and all TMs and HMs. Some Pokémon scholars believe Mew to be the ancestor of all existing Pokémon, but the idea is debatable.
Move Tutor moves really didn't have much prevalence until Emerald, and still aren't as iconic as TMs/HMs. In FireRed/LeafGreen, where Hydro Cannon and friends were introduced, besides the three starter-exclusive tutor moves, they existed exclusively to fill in the roles of removed TMs in Red/Blue. A move like Soft-Boiled for instance, which were TMs prior, only distributed to 4 Pokémon lines, including Mew itself, in FireRed/LeafGreen, and could only be learnt by Chansey and Mew in Red/Blue. Most Move Tutor moves Mew can learn seem, besides in later games, to be by association with TMs than by being an innate feature.
There's also the case with signature moves like Volt Attack and Dragon Ascent being available through Move Tutor, which reveals Game Freak clearly intended for Mew to not learn every Move Tutor move. It makes more sense from a game perspective, as moves likes Relic Song and Secret Sword are tied to a Pokémon's transformation.
It's worth noting there is a Move Tutor in Pokémon XD explicitly for Mew itself that does not teach it the three starter-exclusive moves, cementing Mew's exclusion from learning these moves was intentionally done, rather than them forgetting to include Mew.
