MNT/CI: switch away from deprecated save-always directive for actions…

…/cache

.github/workflows/docs.yml

@@ -60,12 +60,13 @@ jobs:
         run: |
           mkdir doc_cache  # make sure cache dir exists
 
-      - name: Cache FastF1
-        uses: actions/cache@v4
+      - name: Restore cache for FastF1
+        id: cache-doc-restore
+        uses: actions/cache/restore@v4
         with:
-          save-always: true
           path: ./doc_cache
-          key: fastf1-doc-cache-${{ hashFiles('*.*') }}
+           # Restore any matching cache independent of hash suffix. We cannot
+           # now if anything has changed at this stage.
           restore-keys: |
             fastf1-doc-cache
 
@@ -94,6 +95,15 @@ jobs:
         with:
           path: docs/_build/html/
 
+      - name: Save cache for FastF1
+        id: cache-doc-save
+        # Save the cache even in case of a failure but only if the content of
+        # the cached directory has changed.
+        if: always() && steps.cache-doc-restore.outputs.cache-matched-key != hashFiles('./doc_cache/**/*.*')
+        uses: actions/cache/save@v4
+        with:
+          keys: fastf1-doc-cache-${{ hashFiles('./doc_cache/**/*.*') }}
+          path: ./doc_cache
 
   deploy:
     if: (github.event_name == 'release') || inputs.publish