Make dependency installation like static CI workflow (#26)

.github/workflows/publish_docs.yml

@@ -24,6 +24,9 @@ jobs:
           path: .cache
           restore-keys: |
             mkdocs-material-
-      - run: pip install uv
-      - run: uv pip install ".[docs]"
+      - name: Install dependencies
+        run: |
+          python -m pip install --upgrade pip
+          pip install uv
+          python -m uv pip install ".[docs]"
       - run: mkdocs gh-deploy --force