The Steam client works natively on Linux. It ships its own version of Wine, called Proton and many games work well. They are doing lots of work to get the remaining games working in preparation for the launch of Steam Deck.

https://www.protondb.com/

Is it still 32bit?

Yes, same as on Windows.

From my experience:

Linux > Steam > Proton > Windows Game

works better than

Linux > Wine > Steam > Windows Game

There's really no reason to be running Steam in Wine when Steam runs natively within Linux and Proton does the work for you for each individual game.

I can vouch for Proton. In some games, I can even get more FPS running on Proton/Vulcan DX emulation than natively on windows. One such example is Path of Exile. I should totally NOT be playing this game..

Steam Proton is the way to do it now.