mise does not operate well under GitBash on Windows

[zartc]

As a user of GitBash (which comes with Git for Windows), I installed the 2025.1.0 Windows-x64 (ef6936a 2025-01-01).
The program works fine, but it produces paths that are incompatible with GitBash. Any command that updates the PATH variable (including eval $(mise activate bash)) corrupts the GitBash terminal session, rendering it unusable because GitBash cannot find any commands anymore due to the corrupted PATH variable.

The problem:

mise outputs paths in Windows format: C:\Program Files\Git\mingw64\bin;C:\Program Files\Git\usr\local\bin;C:\Program Files\Git\usr\bin using the C: prefix, the \ directory separator, and the ; path separator. However, GitBash expects paths to be in Linux format: using /c/ prefix, / directory separator, and : path separator.

One element of solution:

When running under GitBash ($OSTYPE == "msys"), paths generated by mise should be in Linux format using the / and : separators. In addition, paths pointing to directories inside the GitBash installation directory should be without the C:\Program Files\Git prefix, so that they are seen as absolute paths inside the Linux VFS. For example, C:\Program Files\Git\mingw64\bin => /mingw64/bin, C:\Program Files\Git\usr\bin => /usr/bin.