Add Linux build CI (#7581)

Release Notes:

- N/A

.github/workflows/release_nightly.yml

@@ -31,6 +31,9 @@ jobs:
             - name: Run style checks
               uses: ./.github/actions/check_style
 
+            - name: Run clippy
+              shell: bash -euxo pipefail {0}
+              run: script/clippy
     tests:
         name: Run tests
         if: github.repository_owner == 'zed-industries'