Get `print-api` to work on the standard library

I tried to run https://github.com/Kleidukos/print-api on the standard library to obtain a machine readable summary of the public API.
I tried this with `GHC-9.12.2`, but unfortunately I ran into issue https://github.com/Kleidukos/print-api/issues/40 and only get a summary of exposed instances.

We need to figure out a way to run `print-api` on the repository.

Start by reproducing the reported print-api run against the standard library with GHC-9.12.2, then read print-api issue 40 to understand why only exposed instances are summarized. Investigate the repository setup needed for print-api and verify that it produces a machine-readable public API summary for the standard library.

Written by the indexing model from the issue text.