docs: add documentation to supabase_flutter readme

Author: Vinzent03

packages/supabase_flutter/README.md

@@ -596,6 +596,36 @@ Supabase.initialize(
 );
 ```
 
+## Logging
+
+All Supabase packages use the [logging](https://pub.dev/packages/logging) package to log information. Each sub-package has its own logger instance. You can listen to logs and set custom log levels for each logger.
+
+In debug mode, or depending on the value for `debug` from `Supabase.initialize()`, records with `Level.INFO` and above are printed to the console.
+
+Records containing sensitive data like access tokens and which requests are made are logged with `Level.FINEST`, so you can handle them accordingly.
+
+### Listen to all Supabase logs
+
+```dart
+import 'package:logging/logging.dart';
+
+final supabaseLogger = Logger('supabase');
+supabaseLogger.level = Level.ALL; // custom log level filtering, default is Level.INFO
+supabaseLogger.onRecord.listen((record) {
+    print('${record.level.name}: ${record.time}: ${record.message}');
+});
+```
+
+### Sub-package loggers
+
+- `supabase_flutter`: `Logger('supabase.supabase_flutter')`
+- `supabase`: `Logger('supabase.supabase')`
+- `postgrest`: `Logger('supabase.postgrest')`
+- `gotrue`: `Logger('supabase.gotrue')`
+- `realtime_client`: `Logger('supabase.realtime')`
+- `storage_client`: `Logger('supabase.storage')`
+- `functions_client`: `Logger('supabase.functions')`
+
 ---
 
 ## Migrating Guide

packages/supabase_flutter/lib/src/supabase.dart

@@ -70,7 +70,7 @@ class Supabase {
   /// PKCE flow uses shared preferences for storing the code verifier by default.
   /// Pass a custom storage to [pkceAsyncStorage] to override the behavior.
   ///
-  /// If [debug] is set to `true`, debug logs will be printed in debug console.
+  /// If [debug] is set to `true`, debug logs will be printed in debug console. Default is `kDebugMode`.
   static Future<Supabase> initialize({
     required String url,
     required String anonKey,