A lot of Frontier keeps working while you are looking at something else, and "is it actually running?" should never be a guess. The System Status readout in Settings answers it: a single pill that rolls up to Healthy, Degraded or Offline, which opens into a row per moving part.
What you see there is the app's own listeners, including the encrypted one behind Remote Access; the two background loops — the Scheduler, which fires one-off scheduled threads, and the Conductor, which re-runs your Agents — each showing whether it is running, stopped or overdue for a tick; and whether Frontier is registered with the coding agent you run through, which is what lets it use Frontier's own tools.
A loop that shows as running while the master automation switch is off is not a fault — it says so in as many words. That switch is the first thing to check when an agent seems quiet; see Recover from a stuck agent.
Runs themselves are visible wherever they happen: a workspace row shows its agent state at a glance, and any run in progress can be stopped from the "✕" on its own status pill. For the full record of what a run was told and what it did, see Reading the Audit Trail.