Fix: record started_at for background agent tasks so duration is reported

[nankingjing]

Problem

Background agent tasks never have runtime.started_at set, so their run
duration is silently lost. Background bash tasks set it correctly.

The only place started_at is ever assigned is the bash worker startup
(background/worker.py):

runtime.status = "starting"
runtime.worker_pid = os.getpid()
runtime.started_at = time.time()

Agent tasks reach the running state through BackgroundTaskManager._mark_task_running
(called from background/agent_runner.py), which set every startup field
except started_at:

runtime.status = "running"
runtime.updated_at = time.time()
runtime.heartbeat_at = runtime.updated_at
runtime.failure_reason = None

Since TaskRuntime.started_at defaults to None (background/models.py), agent
tasks keep started_at is None for their whole lifetime.

Impact

Downstream consumers guard on started_at, so for agent tasks they silently
degrade:

• publish_terminal_notifications computes duration_s = None, so the completion
  notification omits the Duration: … line that bash tasks show.
• _mark_task_completed / _mark_task_failed / _mark_task_timed_out /
  _mark_task_killed all gate telemetry on
  if runtime.started_at and runtime.finished_at:, which is never true for agent
  tasks — so the background_task_completed event (with duration_s) is never
  emitted for them.

Fix

Record the first transition into running as the start time in
_mark_task_running, mirroring what the bash worker does. The assignment is
guarded by started_at is None because _mark_task_running is also invoked
again after each approval is resolved; overwriting would otherwise shrink the
measured duration to the last approval gap.

runtime.status = "running"
runtime.updated_at = time.time()
if runtime.started_at is None:
    runtime.started_at = runtime.updated_at
runtime.heartbeat_at = runtime.updated_at

This has no effect on bash tasks (they don't go through _mark_task_running) and
is a no-op for tasks that already reached a terminal state (the early return
guarding terminal status is untouched).

Test

Adds test_mark_task_running_sets_started_at_once, asserting that the first
_mark_task_running sets started_at, a subsequent re-mark (e.g. after an
approval) preserves it, and completion then yields finished_at >= started_at.

Verification

• python -m py_compile on both changed files: passes.
• New/existing tests verified by reading; not executed in my environment
  (runtime deps such as kosong/kaos were not installable here).

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[devin-ai-integration]

✅ Devin Review: No Issues Found

Devin Review analyzed this PR and found no bugs or issues to report.