Rewrite GH action

Google's instructions are broken as they only work for Dart packages but
not Flutter plugins.

.github/workflows/publish.yml

@@ -7,6 +7,26 @@ on:
 
 jobs:
   publish:
+
     permissions:
       id-token: write # This is required for requesting the JWT
-    uses: dart-lang/setup-dart/.github/workflows/publish.yml@v1
+
+    steps:
+      - name: Clone repository
+        uses: actions/checkout@v3
+
+      # This step adds the auth token for pub.dev
+      - name: Set up Dart
+        uses: dart-lang/setup-dart@v1
+        with:
+          sdk: stable
+
+      - name: Set up Flutter
+        uses: subosito/flutter-action@v2
+        with:
+          channel: stable
+          cache: true
+
+      - name: Publish to pub.dev
+        id: pub_release
+        uses: leancodepl/mobile-tools/.github/actions/pub-release@pub-release-v1