They can (source myself)

Just use Proton, although you might need to copy the Linux save to the Windows save location.
Starbreeze seperated them, because the Linux version was running on an older (more buggier) engine version.

Use Proton!, I'd also recommend you download GE from Github for optimal performance.

I've been looking for a very long time and for me the only solution that currently works to launch "Payday 2":

On Linux: In the game properties choose "Experimental Proton".

Then put this command in the properties of "Payday 2" in "General":

PROTON_USE_WINED3D=1 %command%