server: embed web SPA at /, wire build pipeline

- Add internal/server/web/embed.go with //go:embed all:dist and a
  SPA fallback shim: file-not-found → serve index.html at 200.
- Commit dist/.gitkeep and dist/index.html (placeholder) so go build
  works on a fresh clone; real build output stays gitignored.
- Mount web.Handler() as GET /* catch-all in server.go after /api/v1
  so API routes and probe endpoints shadow the wildcard.
- Add three server tests: ServesSPAAtRoot, SPAFallbackForNonAPIPath,
  APIPathsBypassSPA; update NotFoundReturnsProblemJSON for SPA era.
- Extend Justfile with web-{install,dev,build,test,lint,clean} targets;
  build now depends on web-build.
- Add node:20-alpine web-builder stage to Dockerfile; COPY dist into
  the Go builder stage before compiling.