[doc] fix workflow (RustPython#7021)

Author: youknowone

.github/workflows/update-doc-db.yml

@@ -2,6 +2,7 @@ name: Update doc DB
 
 permissions:
   contents: write
+  pull-requests: write
 
 on:
   workflow_dispatch:
@@ -10,10 +11,10 @@ on:
         description: Target python version to generate doc db for
         type: string
         default: "3.14.3"
-      ref:
-        description: Branch to commit to (leave empty for current branch)
+      base-ref:
+        description: Base branch to create the update branch from
         type: string
-        default: ""
+        default: "main"
 
 defaults:
   run:
@@ -56,9 +57,12 @@ jobs:
     steps:
       - uses: actions/checkout@0c366fd6a839edf440554fa01a7085ccba70ac98 # v6.0.1
         with:
-          ref: ${{ inputs.ref || github.ref }}
+          ref: ${{ inputs.base-ref }}
           token: ${{ secrets.AUTO_COMMIT_PAT }}
 
+      - name: Create update branch
+        run: git switch -c update-doc-${{ inputs.python-version }}
+
       - name: Download generated doc DBs
         uses: actions/download-artifact@37930b1c2abaa49bbe596cd826c3c89aef350131 # v7.0.0
         with:
@@ -96,13 +100,18 @@ jobs:
           retention-days: 7
           overwrite: true
 
-      - name: Commit and push (non-main branches only)
-        if: github.ref != 'refs/heads/main' && inputs.ref != 'main'
+      - name: Commit, push and create PR
+        env:
+          GH_TOKEN: ${{ secrets.AUTO_COMMIT_PAT }}
         run: |
           git config user.name "github-actions[bot]"
           git config user.email "github-actions[bot]@users.noreply.github.com"
           if [ -n "$(git status --porcelain)" ]; then
             git add crates/doc/src/data.inc.rs
             git commit -m "Update doc DB for CPython ${{ inputs.python-version }}"
-            git push
+            git push -u origin HEAD
+            gh pr create \
+              --base ${{ inputs.base-ref }} \
+              --title "Update doc DB for CPython ${{ inputs.python-version }}" \
+              --body "Auto-generated by update-doc-db workflow."
           fi