Use reusable WF for deploy-docs.yml

(cherry picked from commit 85d3284834)

.github/workflows/deploy-docs.yml

@@ -1,4 +1,5 @@
 name: Deploy Docs
+
 on:
   push:
     branches:
@@ -7,34 +8,12 @@ on:
     tags:
       - '**'
 
-  repository_dispatch:
-    types: request-build-reference # legacy
-  #schedule:
-  #- cron: '0 10 * * *' # Once per day at 10am UTC
   workflow_dispatch:
 
 permissions:
   actions: write
 
-env:
-  GH_TOKEN: ${{ secrets.GITHUB_TOKEN }}
-
 jobs:
   dispatch-docs-build:
-    runs-on: ubuntu-latest
     if: github.repository_owner == 'spring-projects'
-    steps:
-      - name: Checkout
-        uses: actions/checkout@v4
-        with:
-          ref: docs-build
-          fetch-depth: 1
-          show-progress: false
-
-      - name: Dispatch (partial build)
-        if: github.ref_type == 'branch'
-        run: gh workflow run deploy-docs.yml -r $(git rev-parse --abbrev-ref HEAD) -f build-refname=${{ github.ref_name }}
-
-      - name: Dispatch (full build)
-        if: github.ref_type == 'tag'
-        run: gh workflow run deploy-docs.yml -r $(git rev-parse --abbrev-ref HEAD)
+    uses: spring-io/spring-github-workflows/.github/workflows/spring-deploy-docs.yml@main