Observation: So architecturally, Agent sounds like the "inverse Scheduler" that lives in client's infra. Because Prefect cloud is not allowed to tunnel into client infra, Agent fulfills the role of being an extension of the cloud Scheduler that resides in client infra.

Yes exactly and this way we never see your code or data. This is called the hybrid model in our docs

I think the analogy of inverse scheduler may be confusing because the Scheduler service is part of the orchestration layer. A more helpful model would be to think of: • Prefect Cloud as your orchestration layer or orchestration API telling agents what to do, when, and how • Agents as your execution layer polling the orchestration API for work, executing the work and reporting the state of it to the orchestration API