iOS UX: agent can show typing while profile remains offline after reconnect

## Summary

On iOS, an agent can visibly be typing/working in a channel while its profile reports **Offline**, especially after the phone reconnects to the relay. This is a UX consistency bug: two live indicators for the same agent disagree, making an active hosted agent look unavailable.

## Steps to reproduce

1. Run an agent from Buzz Desktop or another hosted machine and join the same channel on iOS.
2. Disconnect/reconnect the iPhone client, or open it after the agent's latest presence event was already published.
3. Trigger the agent so iOS shows it typing/working.
4. Open the agent profile on iOS.
5. Observe that the profile can still show **Offline**.

## Expected behavior

- A reconnect should restore the latest non-expired presence state instead of waiting indefinitely for a future presence publication.
- If current channel typing/working telemetry proves the agent is active, iOS should not simultaneously present it as offline.
- Presence, typing, and activity surfaces should converge on a clear current state without treating typing as durable presence after it expires.

## Current implementation

- [`presence_cache_provider.dart`](https://github.com/block/buzz/blob/2ea9385015fb922de2adf0a53e86fc5a21d07b90/mobile/lib/features/profile/presence_cache_provider.dart#L8-L46) documents that there is no historical/REST backstop and `track()` performs no fetch; the cache only receives future live kind `20001` events.
- [`user_profile_sheet.dart`](https://github.com/block/buzz/blob/2ea9385015fb922de2adf0a53e86fc5a21d07b90/mobile/lib/features/profile/user_profile_sheet.dart#L50-L80) defaults a missing cache entry to `offline`.
- [`working_bots_provider.dart`](https://github.com/block/buzz/blob/2ea9385015fb922de2adf0a53e86fc5a21d07b90/mobile/lib/features/channels/agent_activity/working_bots_provider.dart#L6-L27) independently derives working agents from channel typing events, which permits the contradictory UI state.

## UX impact

Users cannot trust agent availability on iOS and may avoid opening or messaging an agent that is visibly working. This overlaps the presence symptom reported for Android in #2971, but this issue is specifically the iOS reconnect plus typing/offline contradiction.

Related client UX: #5062.

Start by reading mobile/lib/features/profile/presence_cache_provider.dart, then compare its reconnect behavior with mobile/lib/features/profile/user_profile_sheet.dart and mobile/lib/features/channels/agent_activity/working_bots_provider.dart. Trace how cached presence and channel typing events reach the iOS UI. Done means reconnecting restores a current non-expired presence state and typing does not leave the profile showing Offline, while expired typing is not treated as durable presence.

Written by the indexing model from the issue text.