I did a quick review.
This project uses PQescapeLiteral() and asprintf() to build queries. I'd recommend prepared statements over this approach (which is how the MySQL backend builds queries).
It doesn't implement anything but write() and free() yet, so it's not actually functional.
Unfortunately I believe this would clobber the library license (GPLv3 on this Postgres plugin vs GPLv2 with a linking exception for libgit). With this in mind I'd probably just recommend a rewrite. It's not that much code.
Update: it looks like the libgit2 backends aren't well maintained: https://github.com/libgit2/libgit2-backends/issues/13#issuec...