check that patches are not broken (#12457)

# Objective

- Fixes #12441 
- check that patches are still working

## Solution

- Apply all patches then build Bevy

.github/workflows/validation-jobs.yml

@@ -286,3 +286,31 @@ jobs:
         run: sudo apt-get update; sudo apt-get install --no-install-recommends libasound2-dev libudev-dev
       - name: Run cargo udeps
         run: cargo udeps
+
+  check-example-showcase-patches-still-work:
+    if: ${{ github.event_name == 'merge_group' }}
+    runs-on: ubuntu-latest
+    timeout-minutes: 30
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/cache@v4
+        with:
+          path: |
+            ~/.cargo/bin/
+            ~/.cargo/registry/index/
+            ~/.cargo/registry/cache/
+            ~/.cargo/git/db/
+            target/
+          key: ${{ runner.os }}-cargo-check-showcase-patches-${{ hashFiles('**/Cargo.toml') }}
+      - uses: dtolnay/rust-toolchain@stable
+      - name: Installs cargo-udeps
+        run: cargo install --force cargo-udeps
+      - name: Install alsa and udev
+        run: sudo apt-get update; sudo apt-get install --no-install-recommends libasound2-dev libudev-dev
+      - name: Apply patches
+        run: |
+          for patch in tools/example-showcase/*.patch; do
+            git apply --ignore-whitespace $patch
+          done
+      - name: Build with patches
+        run: cargo build