bridge: Remove build step from CI workflow (#1347)

There is no need to run `cargo build` separately from `cargo test` and
`cargo clippy`. The former command already builds the library with and
without `cfg(test)` (for unit tests and integration tests,
respectively).

Also rename some CI steps to make it more obvious what they're doing.

.github/workflows/bridge-ci.yml

@@ -63,7 +63,11 @@ jobs:
 
     - uses: taiki-e/install-action@nextest
 
-    - name: Install dependencies
+    - name: Clippy
+      run: cargo clippy --locked --all-targets --all-features -- -D warnings
+      working-directory: bridge
+
+    - name: Install system dependencies
       # Packages should align with whatever is in the bridge/Dockerfile
       run: |
         sudo apt-get install -y \
@@ -74,22 +78,14 @@ jobs:
           pkg-config=0.29.* \
           zlib1g-dev=1:*
 
-    - name: Build
-      run: cargo build --locked
-      working-directory: bridge
-
-    - name: Start dependencies
+    - name: Start required services
       run: docker compose -f "bridge/testing-docker-compose.yml" up -d
 
-    - name: Clippy
-      run: cargo clippy --all-targets --all-features -- -D warnings
-      working-directory: bridge
-
     - name: Run tests
       working-directory: bridge
       run: ./run-tests.sh
 
-    - name: Stop dependencies
+    - name: Stop required services
       run: docker compose -f "bridge/testing-docker-compose.yml" down
 
 #  deny-check: