[Noir, TS, C++] App circuit should accept `start_counter`, maintain inner counter, and output `end_counter`

[dbanks12]

Comments from pairing: https://github.com/AztecProtocol/aztec-packages/tree/db/brainstorming-ordering

1. Update PrivateCircuitInputs to include start_sideeffect_counter
2. Add inner sideeffect_counter that is updated for each side-effect operation
3. Update PrivateCircuitPublicInputs to include both start/end_sideeffect_counters

Do not worry about constraining these in the kernel as a part of this task.