[Fix] Telegram working status disappears during active Fast turns

[roomote-roomote]

​Opened on behalf of @daniel-lxs. Follow up by mentioning @roomote-roomote, in the web UI, or in Telegram.

What changed

• Restore Telegram Fast working activity after a managed topic title or icon update clears the native draft during an active parent turn.
• Reassert parent-turn activity after Telegram delegated-task kickoff and live-status writes, including failed launch attempts that may already have posted provider output.
• Keep the existing 300 ms debounce and settlement fencing, so only an active parent turn can restart the indicator and delegated task lifetime never owns it.
• Add a regression that reproduces the missing post-title draft and coverage for successful and failed draft-clearing operations.

Why this change was made

Telegram clears its native draft when the bot emits another update in the conversation. Fast topic metadata and delegated-task status writes could therefore remove Roomote is working... while the parent session was still reasoning, with the next communication reply appearing to start the indicator.

Impact

Telegram users retain visible Fast activity across provider-side updates until the parent turn genuinely settles. The full SDK test suite, focused lifecycle tests, SDK type checks, and repository pre-push gates pass; browser proof is not applicable to Telegram Bot API draft behavior.

[roomote-community]

No code issues found. See task

_{Reviewed 8f4b319}