Do I have a Bad GFCI Circuit Breaker?
I gather you have the panel cover off?
First, you cannot test any GFCI device while anything is plugged into it or on the LOAD terminals.  All wires must be removed from the LOAD terminals.
Once that’s done, we can now do a clear test of the GFCI.  For a breaker, turn it all the way off, then all the way on.  Don’t try to go straight from “tripped” to “on”, that will not work.  Once it is on, then you press the TEST button and see if you get a trip.  Then to OFF then to ON, to reset.
If the GFCI breaker responds correctly when you do that, then the breaker is not faulty.  It is doing its job, tripping due to a fault in wiring or devices. Now you divide and conquer.
The trick with “divide and conquer” with GFCI is that you must isolate BOTH hot AND neutral.  Simply breaking hot is not enough.
You must also be very careful in boxes that have multiple circuits in them.  For instance, sometimes a multi-light switch box has circuit 1’s power coming into it to run some switches, and then a switch loop for a light from circuit 2.  Goober says “I want to put a smart switch on that switch-loop”, so uses the always-hot and switched-hot from the switch loop, and steals neutral from circuit 1.  GFCIs won’t tolerate that.