You would need to reinstall your games on Linux, to answer your question. Steam and Heroic Games Launcher make this process quite painless, but yeah, still gotta do it. NTFS supports ignoring upper/lowercase, whereas Linux (and other Unix-y systems) do not, at least by default. This can cause all kinds of weird issues down the line.

Now that said, one thing you could do is make a new steam library on Windows to a drive or partition formatted as ExFAT, then use Steam on Windows to transfer your games to that new library. If you did that, I think you could simply add that steam library to your instance of steam running on Linux Mint. Combined with setting steam to use Proton for any Windows game (it's just one checkbox to do so), I think maybe you'd be in business.

I run all my games through the Steam Proton compatibility layer and don’t miss Windows for anything. I don’t play multiplayer games outside of Marvel Rivals though so your mileage may vary. Single player games perform flawlessly.

Try dual booting for that extra piece of mins but if you’re anything like me and only do text editing, gaming, and web browsing on your machine, you might not need to stick to Windows at all.

It's a bit advanced, but I have a GPU in my server that doubles as a home theater / couch gaming thing. I PCI passthrough the GPU to a windows VM where I get near baremetal performamce.
It runs ontop of proxmox and has a bunch of containers and VMs for my other stuff.
Currently, the linux part is headless, as in I don't need a screen for the linux stuff on there, but it'd be a matter of hooking up the onboards graphics to another monitor input.
I like the idea because unlike dualboot, it all runs at the same time.
My other desktop's mobo has issues with vfio and iommu groups so I can't really do this on that other machine, but for my next build, good iommu groups will be a deciding factor.
I'd love to have a similar setup for my desktop and just switch monitor inputs or KB/mouse USB switch between both.

Yes. Dual boot, or even simpler, try running your games in Windows VM in Linux. Performance hit should be minimal.

You can dual boot both Windows and Linux, and the reboot to Windows when you want to play games, and reboot to Linux for other stuff.

A bit of work, and extra space needed, but you can easily do that.