Replace PL/pgSQL functions with C implementations

PL/pgSQL functions are hard to maintain because they need to be redefined every time. It is hard to figure out which file the latest version is defined. In our current upgrade infrastructure, changes also cannot be tracked through version control.

More importantly, changes to PL/pgSQL functions require extension updates. This makes backporting impractical, since we'd need to support different upgrade paths. It also makes changes more difficult to test since you need to drop and recreate the extension.