Linux

In general, Microsoft doesn't support many filesystem formats at all. In the same way you shouldn't attempt to cross-run a steam library from Windows on Linux, you really shouldn't do from Linux to Windows. It's in part due to how permissions, execution flags, filesystem case sensitivity, file metadata, is interpreted by Windows applications vs. Unix-like applications. There will be issues going either way when using foreign filesystems in complex tasks.

While it should be expected that the files will have the same contents where they are actually the same (i.e. a Proton game will be the same as a Windows game as it comes from the same steam depot), there is a good chance that translation of interpretation isn't to be 1:1 on either side. Furthermore with using Steam libraries, Steam includes additional data beyond just the game files, which is likely why they are invalidated. A significant portion of visible cross-os portability issues is due to many applications like Steam using OS-specific file structures. More than likely Steam is going to intentionally make the library metadata not fully compatible between Linux and Windows Steam and force validation before launch because there is a good chance the games aren't even compatible builds or otherwise have additional compatibility content dragged along (such as Proton WINE prefixes that are to be completely ignored when launching from actual Windows or having additional libraries, modded executable binaries that have platform-oriented patches).

If you seriously want to run a cross-share of a Steam Library between Linux and Windows, you should really utilize Steam Cloud save. If you want to "deduplicate" your games, your best bet would be if you can open the foreign fs and have a compatible copy of the game, to simply clone the game files to the current filesystem and remove from remote rather than attempt to force a multi-os single-partition shared library. You are less likely to destroy your Steam library if you treat the actual libraries separate, but move the games like they were downloaded externally. Barring being able to do that, just don't cross-share games. Simply reboot into the OS that has the game you want to play instead.