generate and install pkg-config file (mpir.pc)

[GitMensch]

This was added to GMP 6.2 and something similar would be useful to have in MPIR, too.
For the changes related to this see https://gmplib.org/repo/gmp-6.2/log?rev=pkg , you should be able to install this with a name change from gmp->mpir (ideally installing a copy as gmp.pc if --enable-gmp-compat is active).

[dimpase]

probably mpir-gmp.pc would be more appropriate for the compat case.

[GitMensch]

probably mpir-gmp.pc would be more appropriate for the compat case.

I've thought about that but I think gmp-compat should use gmp.pc - because it installs the libraries and headers with the same name and is explicit done as GMP drop-in - and packages looking for gmp would not check mpir-gmp.
Either you want both, then you'll have "pure" GMP and MPIR next to another with different names or you want "gmp interface, no matter how", in this case (and only in this one) you'd use MPIR with gmp-compat.