This won’t probably help much 
and I hope Windows/Linux Experts out here will chime in but I stumbled upon a very old topic (2021 old ) of someone running into something similar with a somewhat similar setup (exFAT hard drive and dual boot Windows + Linux): All Markdown Files Corrupted
Obsidian has evolved a lot since then though 
.
Maybe it could be worth to share the debug info of Obsidian (available in the command palette) you use on each OS ?