e2e: wait for repo_status=ready and bump test timeout

Two issues uncovered by the page-snapshot dump after the agent
state-dir fix:

* The host page server-renders `Run backup now` as disabled
  while repo_status != ready, and the page has no live-refresh
  on that field. The test was navigating right after status
  flipped to 'online' but before auto-init had completed (~3s
  later), so the rendered HTML still showed init_running and
  the click was a no-op. Wait for repo_status === 'ready'
  before navigating.

* playwright.config.ts pinned the per-test timeout at 60s,
  but the test itself uses 60s + 120s of internal waits.
  Bump to 240s so the test fails on real regressions instead
  of timing out on its own internal budget.

Renamed the test description away from "under a minute" since
it overpromises against the new timeout. The performance SLO
belongs in a separate test if we want to assert it.

e2e/playwright/tests/lib/server.ts

@@ -10,6 +10,7 @@ export interface HostJSON {
     id: string;
     name: string;
     status: string;
+    repo_status?: string;
     last_backup_status?: string;
 }