CI - Add cargo ci dep-check and remove unused deps

.github/workflows/ci.yml

@@ -1627,3 +1627,29 @@ jobs:
       # - name: Print rows in the user table
       #   if: always()
       #   run: spacetime sql quickstart-chat "SELECT * FROM user"
+
+  dep_check:
+    needs: [merge_queue_noop]
+    if: ${{ needs.merge_queue_noop.outputs.skip != 'true' }}
+    name: Dependency Check
+    runs-on: spacetimedb-new-runner-2
+    env:
+      CARGO_TARGET_DIR: ${{ github.workspace }}/target
+      RUST_BACKTRACE: full
+    steps:
+      - name: Checkout sources
+        uses: actions/checkout@v4
+
+      - uses: dsherret/rust-toolchain-file@v1
+      - name: Set default rust toolchain
+        run: rustup default $(rustup show active-toolchain | cut -d' ' -f1)
+      - run: echo ::add-matcher::.github/workflows/rust_matcher.json
+
+      - name: Install Rust 1.95 for cargo-shear
+        run: rustup toolchain install 1.95.0 --profile minimal
+
+      - name: Install cargo-shear
+        run: cargo +1.95.0 install cargo-shear --locked
+
+      - name: Run dependency check
+        run: cargo ci dep-check