Obviously, you won't be able to use your Windows Steam binary on Linux. I mean, it's an attempt you can make but why doing a ridiculously thing when you can have it simpler, amirite?

As for that "simpler", install Steam for Linux, then treat your existing library as "actually installed but appear in Steam as uninstalled" and consult https://psteamhelp.yuanyoumao.com/faqs/view/4578-18A7-C819-8620 You'll have to convert your games partition from NTFS to EXT. Or copy the games library from it's old location on an NTFS partition unto a fresh new EXT partition. Either way, if you want to play Steam games in Linux, they'd better sit on an EXT volume.