I've played Primal Hearts and Hello Lady on the deck so far.
I haven't gotten far into them, but Sugar Style, Study Steady seem to work.
ToHeart2 has issues, but I haven't tried any fixes yet.
It would be better to have a VN compatibility site similar to protondb to track this kind of thing though, since most VNs are not on steam and it'd be a bit silly to try and list compatibility with the thousands of VNs in a plain spreadsheet or forum post.
Unless this has changed, you also need to set a launch parameter for JP locale:
LANG=ja_JP.UTF-8 %command%