perf: build docs on the CI runner with a warm .next cache (#840)

Move `npm run build` out of the Docker image onto the runner, where actions/cache persists .next/cache across runs (the in-Docker build discarded it every time). The image now just packages the prebuilt .next and serves it with `next start`; runtime and the DocSearch entrypoint injection are unchanged.

Also: checkout full history (fetch-depth: 0) so per-page dates are correct, guard buildGitDateMap against shallow clones (correct-or-absent, never wrong), modernise the Docker actions (build-push-action v6, provenance: false), and add a path-filtered pull_request trigger so pipeline changes are validated before merge.

Smoke-tested via isolated build + docker run: serves /, /introduction, /api, sitemap, static assets (200); DocSearch placeholder injection intact.

.dockerignore

@@ -1,10 +1,15 @@
 .git/
 .gitignore
-.next/                # Existing Next.js builds
 .dockerignore
 Dockerfile
 docker-compose.yml
-node_modules/         # Installed inside container
 LICENSE
 README.md
-AUTHORS
+AUTHORS
+
+# Reinstalled inside the image (alpine-native — avoids a glibc/musl mismatch)
+node_modules/
+
+# The built .next output is copied in (built on the CI runner, see
+# build_n_push.yml); only the build cache is excluded — it is not served.
+.next/cache/