What is the last version of postgres with pgadmin 3?
While you may be strongly discouraged from continuing to use pgAdmin 3, there's nothing stopping you if you really want to use it. Below you will see pgAdmin 3 connected to a postgresql 12 instance.



Note however, that you're very much doing this at your own risk, you're going to have to click through a lot of error messages when running in an unsupported setup like this. 

Some pretty obvious in retrospect...




Some just annoying...





In general I find a lot of these errors stem from breaking-change updates to the system catalogs between 9.* and 10+. Whether or not they're deal breakers to using this configuration is left to you. If you do decide to press ahead and try to use this setup, there will be a lot of heartache (for example, pgAdmin 3 as provided just won't run on macOS Catalina, end of discussion).

Around these parts you will hear a lot of the "just use psql" line. I use psql and I love it. But sometimes it's nice to have a GUI. I use pgAdmin 4 and I have a love-hate relationship with it. The pgAdmin line has been "meta-stable" IMO for quite some time and I imagine it will remain so for all but the most power-users for at least a bit.