Mobile shows stale settle/snooze state for an offline machine that my other devices already saw

[ebrardushullovcii]

I use T3 Code on a Mac, a PC and the phone app. A common sequence:

1. On the Mac, I settle or snooze a batch of threads. The PC app is connected to the Mac and updates live.
2. I close the Mac.
3. I open the phone app. It cannot reach the Mac, so it shows its own older cache: the threads I settled are back as unsettled, and snoozed ones are back in the list.

The correct state exists. The PC saw it, and the Mac has it. But no device can give it to the phone, and because of #4852 I can't settle or snooze them again from the phone either. So the threads stay wrong on mobile until the Mac is back on.

This is not a request for offline features. The phone is showing state that is wrong, while the correct state is already on another of my devices.

Smallest version I can think of:

• The relay keeps a "last known lifecycle" row per thread: environment ID, thread ID, settledAt, snoozedUntil, archivedAt, lifecycleUpdatedAt. No titles or messages. The relay already stores more than this per thread in relay_agent_activity_rows for Live Activities.
• The environment sends that row when a thread is settled, snoozed, unsnoozed or archived.
• When an environment is offline, the client reads those rows and applies only the ones newer than its cached shell. They are read-only: the environment still owns the state, and live data always wins once it reconnects.

This only covers T3 Connect environments. For LAN/Tailscale setups, #20279 (a read-only copy stored on another online environment) covers the same need in a different way.

Related: #4852 (actions on an offline environment's threads), #24491 (auto-hide threads from offline environments), #20279.

[juliusmarminge]

Closing as a duplicate of #24530, which tracks the same request. Please follow along there.