After a reload the unified mailbox showed only the active account's mail;
other accounts appeared only once visited. Intermittent (~1 in 14), and
not a timeout - nothing on this path uses setTimeout/AbortSignal/race.
checkAuth awaits only the active account and restores the rest in a
fire-and-forget background loop, registering each client only after
connect() resolves. buildUnifiedAccountClients drops accounts with no
live client (`if (!c) continue`). And isConnected was persisted, so it
rehydrated stale-true: the account passed the isConnected filter while
failing the client lookup, and connectedAccountsSignature already looked
complete at mount so nothing re-fired - and the effects keyed on it only
recompute counts, never the list.
Clear isConnected/hasError on rehydrate so both the filter and the
signature describe this session, and refetch the open unified/cross list
when an account joins the connected set (growth only, not on first
render, not while a search owns the list). Extracted
connectedAccountsGrew so the membership check is testable without
rendering MailApp.
Verified the reset cannot block reconnection: checkAuth reads the full
account list and never filters on isConnected.
Fixes#950