At the best of times, moving steam games is a mess as more and more games use third party download systems.
But also? Going from Windows to Linux is an extra mess.
What I ended up doing to migrate from windows to linux for gaming without taking a poo on my data cap was:
Enable LAN transfers of games in Steam
Install/login to Steam on my linux laptop. If you don’t have a spare PC, this can largely be replaced with a raspberry pi with a big ass external drive attached.
Install the games I want to preserve. Steam is smart enough to realize it is the same files between windows and linux in this case
When that was done, reformat my desktop
Basically do the opposite direction and have my desktop stream the game files from my laptop.
Stuff like warframe was still a full redownload. But helped a lot.