refactor(app): record /btw chats without waiting for the store to load

[Brendonovich]

Summary

Follow-up to #53270. /btw no longer waits for the session's store to load before recording a chat.

• ask() pushes the chat and opens its tab immediately, in one batch, and starts the request. It replaces a Promise + createRoot + abort-signal + two createKeyed watchers that waited for store.ready().
• This is safe because of existing host behaviour:
  • Persisted.update before load already queues, and the queue applies in the same batch that marks the store ready, so the chat lands over the stored value with no ready-but-missing gap.
  • saved(session) returns one stable handle per session for as long as its tab is open.
  • The panel already keeps a not-yet-loaded tab listed but hidden, so the tab isn't dropped before the chat arrives.
• generate() now takes the question as a parameter instead of reading it back from the store, which may still be loading. Retry reads the stored question and passes it in.
• Behaviour change: navigating away from the session (Home, another session) before its store loads now keeps the chat instead of cancelling it. Only closing the session's titlebar tab before load discards it, along with that session's store.
• ask() is now synchronous, so it no longer holds the composer's submit lock.

Validation

• /btw e2e keeper (btw-sidebar.spec.ts): 4 passed.
• packages/app and packages/gui-extensions typechecks, lint:changed, and Prettier passed.
• The queue-before-load store contract is already covered by the extension host component test (extension-host.spec.ts, an update before load applies once it loads). Native desktop was not exercised.