ci: run the check and site workflows on the linux-base runner

Drop the hosted setup-pixi step for the self-hosted runner, install the locked environment in the site workflow, run the quick check before building, and serialize publishes.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

.gitea/workflows/check.yml

@@ -9,13 +9,10 @@ jobs:
     strategy:
       fail-fast: false
       matrix:
-        os: [ubuntu-latest, macos-latest]
+        os: [linux-base]
     runs-on: ${{ matrix.os }}
     steps:
       - uses: actions/checkout@v4
-      - uses: prefix-dev/setup-pixi@v0.9.4
-        with:
-          pixi-version: v0.69.0
       - name: Check the repository
         run: pixi run check
       - name: Stress the reference implementation