fix(app): stop probing the control plane while disconnected

VpnConnection._init() started a 30 s /health poll from the constructor
with no lifecycle gating, so it ran for the life of the app process -
backgrounded, and whether or not the user ever connected. The app is
excluded from its own tunnel, so those requests left in the clear. A
periodic request that fires while the user is deliberately not connected
is an avoidable fingerprint, and rule 60 already ruled probes out:
reachability is meant to be passive.

All it bought was the status dot before the first connect, and it got
that wrong in both directions - "Offline" on a transient resolver
failure against a server that was fine.

Reachability now comes from a session sync that succeeded. serverHealthy
is isConnected && hasSyncedOnce, so a green dot means a working session
rather than a check made beforehand; while disconnected the bar reads
"Ready" and claims nothing either way.

checkHealth() goes with it. Nothing calls it, and leaving a probe helper
in place invites its reuse.

Pinned in test/session_lifecycle_regression_test.dart so it cannot come
back as a tidy-up. flutter analyze clean, 10/10 tests pass.

Co-Authored-By: Claude Opus 5 <[email protected]>

CHANGELOG.md

@@ -5,6 +5,19 @@ Versions follow [semver](https://semver.org/): MAJOR.MINOR.PATCH
 
 ---
 
+## [Unreleased]
+
+### Removed
+- **The background server check while disconnected.** The app no longer contacts
+  the server every 30 seconds while you are not connected to it. Nothing about
+  the connected session changes.
+
+### Changed
+- **The status bar no longer guesses whether the server is up.** It reads
+  "Ready" while disconnected and shows "Online" once a session has synced, so a
+  green dot now means a session that is actually working rather than a
+  reachability check made beforehand.
+
 ## [3.3.8] — 2026-10-17
 
 ### Changed