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.