docs: add automatic release calendar updates in docs (#17531)

.github/workflows/release.yaml

@@ -924,3 +924,55 @@ jobs:
         continue-on-error: true
         run: |
           make sqlc-push
+
+  update-calendar:
+    name: "Update release calendar in docs"
+    runs-on: "ubuntu-latest"
+    needs: [release, publish-homebrew, publish-winget, publish-sqlc]
+    if: ${{ !inputs.dry_run }}
+    permissions:
+      contents: write
+      pull-requests: write
+    steps:
+      - name: Harden Runner
+        uses: step-security/harden-runner@c6295a65d1254861815972266d5933fd6e532bdf # v2.11.1
+        with:
+          egress-policy: audit
+
+      - name: Checkout repository
+        uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683 # v4.2.2
+        with:
+          fetch-depth: 0 # Needed to get all tags for version calculation
+
+      - name: Set up Git
+        run: |
+          git config user.name "Coder CI"
+          git config user.email "cdrci@coder.com"
+
+      - name: Run update script
+        run: |
+          ./scripts/update-release-calendar.sh
+          make fmt/markdown
+
+      - name: Check for changes
+        id: check_changes
+        run: |
+          if git diff --quiet docs/install/releases/index.md; then
+            echo "No changes detected in release calendar."
+            echo "changes=false" >> $GITHUB_OUTPUT
+          else
+            echo "Changes detected in release calendar."
+            echo "changes=true" >> $GITHUB_OUTPUT
+          fi
+
+      - name: Create Pull Request
+        if: steps.check_changes.outputs.changes == 'true'
+        uses: peter-evans/create-pull-request@ff45666b9427631e3450c54a1bcbee4d9ff4d7c0 # v3.0.0
+        with:
+          commit-message: "docs: update release calendar"
+          title: "docs: update release calendar"
+          body: |
+            This PR automatically updates the release calendar in the docs.
+          branch: bot/update-release-calendar
+          delete-branch: true
+          labels: docs