In short
If an operator run is blocked before the AI does any work, it does not count toward your monthly allowance: 30 runs on the free plan, 300 on Pro. The remaining allowance is shown in the operator screen.
What changed
The monthly limit is checked by the database when a run is created, and blocked runs are left out of the count. Scheduled operators use the same allowance, so background work cannot exceed it.
What you will see
The operator screen shows how many runs remain this month and explains when a run was blocked.