GFCI Circuit Breaker 'Test' works, but doesn't trip with plug tester
It sounds like the GFCI is not grounded. This is the proper method to change from a 2 wire / prong system to a 3 prong and be code compliant. Being close to the service panel you can now legally add a ground wire and the tester will trip the GFCI this recently became legal according to the national electric code. You are not required to add the ground but if close why not. The GFCI will still do its job without a ground. I know you said everything was connected but it sounds like an open ground to me.

In an actual life-safety situation that the GFCI protects, the extra current would be flowing through a person to ground (including just about any path from the person to the rest of the world). But with a tester, the extra current is going directly to the ground pin. If that pin is not connected to anything at all then the current doesn't actually flow (not a complete circuit) - and the GFCI doesn't trip.