Move to the layout REPO_POLICIES.md gives (closes #30)

The Go module moves from backend/ to the root (go.mod, go.sum,
.golangci.yml, cmd/, internal/), the page's source to web/, and nginx's
two files to configs/. backend/ is gone: its LICENSE and .dockerignore
are deleted, and its .gitignore entries, README and scripts are folded
into the root ones. script/build builds the server binary after the
frontend; script/run and script/clean move up from backend/script/;
make test, lint, fmt and fmt-check do what the backend's did. Vite's
root is web/ and it still builds into dist/. go.mod ignores
node_modules/, whose npm packages can ship .go files. script/bootstrap
no longer installs gcc, which only the host Go tests needed.

Model: opus-5-5

internal/handlers/healthcheck.go

@@ -0,0 +1,11 @@
+package handlers
+
+import "net/http"
+
+// HandleHealthCheck returns a handler for the health check
+// endpoint.
+func (s *Handlers) HandleHealthCheck() http.HandlerFunc {
+	return func(w http.ResponseWriter, r *http.Request) {
+		s.respondJSON(w, r, s.hc.Healthcheck(), http.StatusOK)
+	}
+}