On Steam Deck, I have three tabs thanks to TabMaster: Installed Games (both Steam and Non-Steam), All Games Owned, and Apps (for Heroic/Geforce Now, etc).
When I finish a game, I file it under a 'completed' category, uninstall the game, and hide it in my library. This also hides it in the 'All Games' library, but I can always pull it up elsewhere.
I also have 'trash' and 'infinite/multiplayer' categories as well, with the multiplayer games not being hidden. I also hide extra bits and pieces (like original versions of remastered games, server/beta programs and so on).
But ultimately: play game, hide game when done.