Backend.max_circuits gives "maximum # of circuits for all instances", not for the chosen one.

[mchan90]

Describe the bug

I used qiskit-ibm-runtime with multiple instances with different maximum circuits allowed. For some reason, I chose one of instance to use. It seems applied well. But, when I call Backend.max_circuits, it gives maximum # of circuits allowed over all instances I have, not the instnace I chose. For example, If I have two instances A and B that allow 300 circuits and 100 circuits, max_circuits gives 300, even if I choose instance B.

Maybe this is intended, not a bug. But it is confusing. I have to visit the IBM quantum webpage, to check real max_circuits. I suggest to modify Backend.max_circuits to give "maximum # of circuits for chosen instance"

Steps to reproduce

1. Prepare IBM account with multiple instance, with different max_circuits.
2. Specify instance for service or backend.
3. call Backend.max_circuits

Expected behavior

gives # of maximum circuits for chosen instance.

Suggested solutions

add a instance filtering procedure in max_circuit routine.

Additional Information

• qiskit-ibm-runtime version:0.12.1
• Python version:3.10.12
• Operating system: WSL 2