Check explain plan of a running query in other session

I am asking myself for a while if there is an easy option (via dictionary views like pg_stat_activity or similar) to check what execution plan was chosen for a long running SQL statement while it is running in a different session?

I have a performance problem in a plpgsql procedure that executes an update within a loop. My guess is that it chose a generic plan instead of bind peeking and then does not use an index.

I am not able to proof my theory, since I don't know how to get the explain plan for it.

For me the easiest would be to check the running statement in a different session and "hook into" the other plpgsql session to check what the optimizer chose.

Is that something I can do easily? If not: What is the PostgreSQL way of doing it?