[3.15] Seed pip caches for docs on main/3.x branches (GH-153127) (#153231)

Co-authored-by: Hugo van Kemenade <1324225+hugovk@users.noreply.github.com>

Author: miss-islington

.github/workflows/reusable-docs.yml

@@ -3,6 +3,17 @@ name: Reusable Docs
 on:
   workflow_call:
   workflow_dispatch:
+  # Pushes to CPython branches seed the pip caches under the exact keys every
+  # docs PR restores from. Without a branch-scoped copy, each PR saves a
+  # duplicate into its own refs/pull/N/merge scope that nothing else can read.
+  push:
+    branches:
+      - main
+      - '3.*'
+    paths:
+      - 'Doc/pylock.toml'
+      - 'Doc/requirements.txt'
+      - '.github/workflows/reusable-docs.yml'
 
 permissions:
   contents: read