docs: refresh README + docs/ for v0.2.0

The README still framed the project as "Phase 5 / pre-v0.1.0" and the
docs predated the v0.2.0 surface (typed BridgeOp, public service
interfaces, port negotiation, pre-migration auto-backup, bridge:export,
periodic auto-update, two new makers, qmltestrunner). Bring them in line
with what's actually shipped, and add badges (release, license, PHP,
Symfony, Qt, FrankenPHP, CI, platform) to the README so the status is
legible at a glance.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

docs/packaging-linux.md

@@ -117,6 +117,17 @@ void BackendConnection::applyUpdate() {
 
 `appImage` is `qgetenv("APPIMAGE")` — the AppImage runtime exports this when an AppImage launches. Outside an AppImage the env is unset and both methods short-circuit with `updateCheckFailed("APPIMAGE env not set; not running from a packaged AppImage")`.
 
+### Periodic check
+
+The supervisor schedules `checkForUpdates()` automatically on the first `Online` transition (10 s after backend ready) and re-arms it every 6 hours by default. PLAN.md §11 *Auto-update* asked for "check on launch and once per N hours; offer install on next restart, never auto-restart" — the periodic check surfaces `updatesAvailable()` for an in-app banner; `applyUpdate()` is still the explicit user-driven trigger and there is no auto-restart.
+
+Two env vars tune it (see [Bundled mode §periodic check](bundled-mode.md#periodic-check)):
+
+- `BRIDGE_AUTO_UPDATE_DISABLE=1` — skip the periodic poll (Q_INVOKABLE methods still work).
+- `BRIDGE_AUTO_UPDATE_PERIOD_MIN=<minutes>` — override the default 360 minutes.
+
+Dev mode skips the periodic check entirely.
+
 ### Appcast (`latest.json`)
 
 CI publishes a `latest.json` next to the release artefacts: