Use uv in publish workflow

Author: tobiasraabe

.github/workflows/publish-to-pypi.yml

@@ -15,18 +15,13 @@ jobs:
     - uses: actions/checkout@de0fac2e4500dabe0009e67214ff5f5447ce83dd # v6
       with:
         persist-credentials: false
-    - name: Set up Python
-      uses: actions/setup-python@a309ff8b426b58ec0e2a45f0f869d46889d02405 # v6
+    - name: Install uv
+      uses: astral-sh/setup-uv@37802adc94f370d6bfd71619e3f0bf239e1f3b78 # v7
       with:
-        python-version: "3.x"
-    - name: Install pypa/build
-      run: >-
-        python3 -m
-        pip install
-        build
-        --user
+        enable-cache: true
+        python-version: "3.13"
     - name: Build a binary wheel and a source tarball
-      run: python3 -m build
+      run: uv build
     - name: Store the distribution packages
       uses: actions/upload-artifact@bbbca2ddaa5d8feaa63e36b76fdaad77386f024f # v7
       with:
@@ -51,8 +46,10 @@ jobs:
       with:
         name: python-package-distributions
         path: dist/
+    - name: Install uv
+      uses: astral-sh/setup-uv@37802adc94f370d6bfd71619e3f0bf239e1f3b78 # v7
     - name: Publish distribution 📦 to PyPI
-      uses: pypa/gh-action-pypi-publish@ed0c53931b1dc9bd32cbe73a98c7f6766f8a527e # release/v1
+      run: uv publish
 
   github-release:
     name: >-