refactor(settings): invert sync logic from whitelist to blacklist

Replace _SYNC_KEYS (37 keys) with _NO_SYNC_KEYS (5 keys) in SettingsHandler.
New settings automatically sync to frontend unless explicitly excluded.

Changes:
- SettingsHandler now syncs all settings except those in _NO_SYNC_KEYS
- Added keys() method to SettingsManager for iteration
- Updated tests to use new behavior

Benefits:
- No more missing keys when adding new settings
- Reduced maintenance burden
- Explicit exclusions for sensitive/internal settings only

Fixes: #86

tests/routes/test_api_snapshots.py

@@ -45,6 +45,9 @@ class DummySettings:
     def set(self, key, value):
         self.data[key] = value
 
+    def keys(self):
+        return self.data.keys()
+
 
 async def noop_async(*_args, **_kwargs):
     """No-op async function."""