Dear Eduard,
I assume it'd be much easier to decide on some old but widespread
Linux distro an base CI on that.
I think it will be difficult to keep such a CI system sane and safe. It is much less of a fuzz to to builds on a years old Cygwin on a modern Windows than to maintain a CI server with a years old Linux. The idea of using repo caches is to archive the state in which things did work once. The point is to maintain compatibility with such a build environment. With Cygwin this is very low effort - just backup the local repo cache and tell the installer to not update the cached version. That's all. You can setup any number of cygwins from different repo caches with a script on one Windows machine. I don't know much about MSys2, but I guess it would be similar.
Best regards,
Michael