I think this is the first time in the 100days project that I've worked on a project that is not my own! Today I added support for JSON requests to Known's Micropub endpoint. I also added support for JSON checkins that OwnYourSwarm sends.
Unfortunately adding Postgres support isn't as easy as switching the PDO driver, because Postgres has significantly different syntax from MySQL (mostly around quote styles, e.g. "foo" for table names and 'foo' for strings, whereas MySQL uses "foo" or 'foo' for strings and `foo` for table names). It would take adding a new file for Postgres support similar to the MySQL file (https://github.com/idno/idno/blob/b748d7765e2a0999fe2bf90f79a816aede366a74/Idno/Data/MySQL.php) you found.