fix(tasks): relay late Slack answers from completed runs

[VojtechBartos]

Problem

When the sandbox agent ends its turn to wait on a background process, the wake-up turn that produces the answer is a background (task-notification) turn. Those never resolved a tracked prompt, so agent-server never relayed them to Slack (fixed in PostHog/code#3704). On this side there is a second hole: a Slack-origin run idling on background work hits the 30-minute inactivity timeout and gets marked completed, and relay_task_run_message skipped every terminal run, so a wake-up answer landing during or shortly after teardown was silently dropped even though the SlackThreadTaskMapping still exists.

Origin: https://posthog.slack.com/archives/C09SK2PAGKF/p1784716116964029

Changes

• relay_task_run_message now accepts runs whose terminal status is COMPLETED; FAILED and CANCELLED runs stay silent since their terminal Slack card is the last word.
• For a completed run the agent-design inline-stream branch is bypassed: the run's workflow is closed and can't receive the agent_text_delta signal, so the message goes through the posthog-code-agent-relay workflow, which only needs the thread mapping.
• Non-terminal runs behave exactly as before.

How did you test this code?

Automated only:

• New: relay accepted for a completed run with a Slack mapping (catches the dropped late background answer).
• New: completed run with agent-design state posts via the relay workflow instead of signaling the closed workflow.
• New (parameterized): failed and cancelled runs with a mapping still skip.
• Full run: pytest products/tasks/backend/tests/test_api.py -k relay_message (10 passed), ruff, file-scoped mypy clean, hogli ci:preflight --fix (0 failures).

Automatic notifications

• Publish to changelog?
• Alert Sales and Marketing teams?

Docs update

Not needed: internal relay behavior, no user-facing workflow change.

🤖 Agent context

Autonomy: Human-driven (agent-assisted)

Built with Claude Code from an investigation of the Slack thread above: the bot answered questions in its transcript but never posted the answers when the work went through a background process. The classic relay is push-based from agent-server on prompt resolution, so the fix has two halves: PostHog/code#3704 makes agent-server relay background turns, and this PR stops the backend from rejecting relays that arrive after the run's inactivity-timeout completion. An alternative of keeping the run alive while background work is pending was considered and deferred as a follow-up with real design surface (heartbeat semantics, caps).

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[scheduled-actions-posthog]

This PR hasn't seen activity in a week! Should it be merged, closed, or further worked on? If you want to keep it open, please remove the stale label – otherwise this will be closed in another week. If you want to permanently keep it open, use the waiting label.

[scheduled-actions-posthog]

This PR hasn't seen activity in a week! Should it be merged, closed, or further worked on? If you want to keep it open, please remove the stale label – otherwise this will be closed in another week. If you want to permanently keep it open, use the waiting label.

[scheduled-actions-posthog]

This PR was closed due to lack of activity. Feel free to reopen if it's still relevant.