refactor: Migrate to maintained badge package

pubspec.lock

@@ -459,14 +459,6 @@ packages:
     description: flutter
     source: sdk
     version: "0.0.0"
-  flutter_app_badger:
-    dependency: "direct main"
-    description:
-      name: flutter_app_badger
-      sha256: "64d4a279bab862ed28850431b9b446b9820aaae0bf363322d51077419f930fa8"
-      url: "https://pub.dev"
-    source: hosted
-    version: "1.5.0"
   flutter_cache_manager:
     dependency: "direct main"
     description:
@@ -605,6 +597,14 @@ packages:
       url: "https://pub.dev"
     source: hosted
     version: "2.4.1"
+  flutter_new_badger:
+    dependency: "direct main"
+    description:
+      name: flutter_new_badger
+      sha256: d3742ace8009663db1ac6ba0377b092f479c35deb33e05514ba05cc0b0a5aaaa
+      url: "https://pub.dev"
+    source: hosted
+    version: "1.1.1"
   flutter_olm:
     dependency: "direct main"
     description:
@@ -2303,5 +2303,5 @@ packages:
     source: hosted
     version: "3.1.2"
 sdks:
-  dart: ">=3.5.0 <4.0.0"
+  dart: ">=3.5.1 <4.0.0"
   flutter: ">=3.24.0"