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Collection Sidequest sometimes, especially in RP Gs or similar. Probably not for your Smash Bros example.
Trophies from Smash Bros are listed under Cosmetic Award, which is less of a collectable per se and more of a "here's a trophy/ribbon/medal for your accomplishment", even if there are a lot of those awards.
Edited by KDGotta Catch Them All seems to be for required items, of which you're required to collect all of them. I can think of tropes like Collection Sidequest for an optional collectible items, and Achievement System for more abstract collectibles, but a general collectible trope seems to be missing.
Make it so we never die, and take the pain awayThere's Follow the Money for the most basic collectible (coins in a Super Mario game, rings in a Sonic the Hedgehog game, bananas in Donkey Kong Country, etc), and also how the level designers will use lines of these collectibles help guide the player.
^^ the page itself sorts Gotta Catch 'Em All into "crucial", "important", and "optional" subcategories when it comes to video games, so optional collectibles should definitely count
Edited by NoUsernameNthing Gotta Catch 'Em All as the you want here.
Collection Sidequest kicks in if there's some sort of in-game reward or acknowledgement of this (even if it's of the Bragging Rights Reward or Cosmetic Award sort)

Basically just collectibles in a game. They may serve a practical purpose in one way, while they're just simply rewards in another. The Trophies and Stickers from the Super Smash Bros. games for example. (Not to be confused with Collect-a-Thon Platformer, a specific genre of games with a specific focus on collectibles to progress.)