I would set up Syncthing, that way you don't have to manually move files around. But yes, if you move the prefix files to Steam Deck, it should work.

Games often don't put the save files in the game data dir but use some random place in documents or the home directory. The library itself will move and be picked up fine but the saves will have to be sync thinged or rcloned or something manually if they're not on steam cloud.

Once you figure out where the save file for the game is on your PC, you can simply switch to desktop mode on the deck and copy them over. I've got an smb share that I used to copy things between devices, but you can also use a flash drive.

For games that doesn't support Steam Cloud for saves etc., or in general moving files over to the Steam Deck from your PC, I highly recommend setting up Syncthing.

It's available on the Discover store in desktop mode and can be set up to run as a service to ensure that it's always running on Steam Deck, if you're so inclined. There's a myriad of guides out there if you search around, should you need help setting it up.