[Backport 1.12] normalize paths when writing a project file (#4444)

[KSepetanc]

Manual backport for #4444 to normalize project paths.

[DilumAluthge]

Thanks!

[DilumAluthge]

@IanButterworth or @KristofferC Would you be able to review this?

[KSepetanc]

The only conflict was in src/Types.jl line 13.
The difference was that in the branch of original PR there was also import atomic_toml_write, create_cachedir_tag.
I found no part of PR relies on that and this is not used in current backport branch so it is removed now.
I doubt tests would pass with missing import statements.