[Fix] Preserve mobile task-panel navigation after refresh

[roomote-roomote]

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

What changed

Mobile users opening a task from a Session's Tasks panel now get a durable ?task=<id> URL. Refreshing the Session keeps the nested task panel open, and closing it clears the task query and returns to the parent Session.

Desktop task-panel behavior remains unchanged, including local one-panel selection and existing URL-selected task switching. Focused behavioral tests cover mobile open/refresh/close and the desktop non-regression.

Why this change was made

Before this fix, a mobile Tasks-panel click only changed local UI state. The browser URL stayed on the parent Session, so refresh or navigation discarded the task output the user had opened.

Impact

Task output navigation is now recoverable and shareable on mobile without changing the Session or task backend contracts. Focused client tests, web typechecking, changed-file lint/format checks, and the full pre-push suite pass. Authenticated visual proof was attempted on the exact final UI but is blocked by the shared five-minute capture deadline; no screenshots or screencasts are claimed, so this pull request remains a draft.

[roomote-community]

No code issues found. See task

_{Reviewed 2bd2fe5}