I've tried Windows exports in nw.js, adding as non-steam game, then running through Proton and that won't work. I've tried native Linux exports and that won't work either.
Both options work for me.
Linux export doesn't require Proton in Compatibility settings. You can even run it from Desktop mode.
Try exporting with older NWjs versions, for example 72 or 75. Also I've seen in some other thread that requesting full-screen with Browser plugin on start of the game may help.