Use database logger for sync protocol

[simolus3]

When we use a worker for the streaming sync implementation, we currently have an independent autoLogger for that. This makes it impossible for users to customize or disable the logs emitted by the worker.

By re-using the logger from the PowerSyncDatabase instead, users can customize the log levels. Closes #225.

Unfortunately this is hard to test without setting up integration tests as it requires the worker. The fix can be verified manually by applying the snippet suggested in #225 in an example project:

diff --git a/demos/supabase-todolist/lib/powersync.dart b/demos/supabase-todolist/lib/powersync.dart
index 166de1b..4e1cbf1 100644
--- a/demos/supabase-todolist/lib/powersync.dart
+++ b/demos/supabase-todolist/lib/powersync.dart
@@ -155,8 +155,13 @@ Future<String> getDatabasePath() async {
 
 Future<void> openDatabase() async {
   // Open the local database
+  hierarchicalLoggingEnabled = true;
+  final logger = Logger('PowerSyncLogger')..level = Level.OFF;
   db = PowerSyncDatabase(
-      schema: schema, path: await getDatabasePath(), logger: attachedLogger);
+    schema: schema,
+    path: await getDatabasePath(),
+    logger: logger,
+  );
   await db.initialize();
 
   await loadSupabase();