Add a Github Action to build code in CI

This adds a CI workflow in Github Actions to verify that the flutter builds compile for all supported platforms.

I tried adding Windows, but it currently fails, so I excluded it from this initial set.

.github/workflows/build.yml

@@ -0,0 +1,76 @@
+name: Build
+
+on:
+  push:
+  pull_request:
+
+jobs:
+  android:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-java@v4
+        with:
+          distribution: "temurin"
+          java-version: "17"
+      - uses: subosito/flutter-action@v2
+        with:
+          channel: "stable"
+          cache: true
+      - name: Cache Gradle
+        uses: actions/cache@v4
+        with:
+          path: |
+            ~/.gradle/caches
+            ~/.gradle/wrapper
+          key: ${{ runner.os }}-gradle-${{ hashFiles('android/gradle/wrapper/gradle-wrapper.properties', 'android/build.gradle', 'android/settings.gradle', 'android/app/build.gradle', 'pubspec.lock') }}
+          restore-keys: |
+            ${{ runner.os }}-gradle-
+      - run: flutter pub get
+      - run: flutter build apk --release --no-pub
+
+  ios:
+    runs-on: macos-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: subosito/flutter-action@v2
+        with:
+          channel: "stable"
+          cache: true
+      - run: flutter pub get
+      - run: flutter build ios --release --no-codesign --no-pub
+
+  linux:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: subosito/flutter-action@v2
+        with:
+          channel: "stable"
+          cache: true
+      - name: Install Linux build deps
+        run: sudo apt-get update && sudo apt-get install -y clang cmake ninja-build pkg-config libgtk-3-dev
+      - run: flutter pub get
+      - run: flutter build linux --release --no-pub
+
+  macos:
+    runs-on: macos-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: subosito/flutter-action@v2
+        with:
+          channel: "stable"
+          cache: true
+      - run: flutter pub get
+      - run: flutter build macos --release --no-pub
+
+  web:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: subosito/flutter-action@v2
+        with:
+          channel: "stable"
+          cache: true
+      - run: flutter pub get
+      - run: flutter build web --release --no-pub