feat(ingestion): expose Prometheus /metrics for brain query latency

Closes infra#50.

Adds an internal/metrics package with a hand-rolled Prometheus
exposition layer (stdlib + sync/atomic only — no new dep) and wraps the
HTTP mux with a timing middleware. Every request emits one observation
on the `brain_query_duration_seconds` histogram labeled by
`path` (request Pattern, low cardinality) and `status` (2xx/3xx/4xx/5xx).

Dependency choice: hand-rolled rather than github.com/prometheus/client_golang
because the surface needed is small (one histogram + bucket constants)
and the repo CLAUDE.md keeps deps stdlib + jwx + testify only. ~150 LOC
of code + tests is cheaper than the chart of transitive prometheus deps.

Endpoints:
- GET /metrics  — OpenMetrics text exposition, no auth (cluster-internal)

Wire format pinned by tests in internal/metrics/metrics_test.go. The
ServiceMonitor that drives the kube-prometheus-stack scrape lives in
infra/k3s/apps/supervisor/ (separate commit on mathias/infra).

After this image deploys, the canary alert from
docs/superpowers/specs/2026-05-homelab-architecture-review.md becomes
wireable:

  histogram_quantile(0.95,
    sum(rate(brain_query_duration_seconds_bucket[5m])) by (le))
    > 1.5 * histogram_quantile(0.95,
        sum(rate(brain_query_duration_seconds_bucket[5m] offset 7d)) by (le))

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

ingestion/internal/metrics/metrics_test.go

@@ -0,0 +1,119 @@
+package metrics
+
+import (
+	"io"
+	"net/http"
+	"net/http/httptest"
+	"strings"
+	"testing"
+	"time"
+)
+
+func TestRegistry_ObserveAndExpose(t *testing.T) {
+	t.Parallel()
+
+	r := New()
+	// Three observations on the same series; one falls into each
+	// representative band.
+	r.Observe("/query", "2xx", 4*time.Millisecond)   // ≤ 5ms
+	r.Observe("/query", "2xx", 20*time.Millisecond)  // ≤ 25ms
+	r.Observe("/query", "2xx", 600*time.Millisecond) // ≤ 1s
+
+	req := httptest.NewRequest(http.MethodGet, "/metrics", nil)
+	rec := httptest.NewRecorder()
+	r.Handler().ServeHTTP(rec, req)
+
+	body := rec.Body.String()
+
+	mustContain := []string{
+		`# TYPE brain_query_duration_seconds histogram`,
+		`brain_query_duration_seconds_bucket{path="/query",status="2xx",le="0.005"} 1`,
+		`brain_query_duration_seconds_bucket{path="/query",status="2xx",le="0.025"} 2`,
+		`brain_query_duration_seconds_bucket{path="/query",status="2xx",le="1.0"} 3`,
+		`brain_query_duration_seconds_bucket{path="/query",status="2xx",le="+Inf"} 3`,
+		`brain_query_duration_seconds_count{path="/query",status="2xx"} 3`,
+	}
+	for _, want := range mustContain {
+		if !strings.Contains(body, want) {
+			t.Errorf("missing line: %q\n--- body ---\n%s", want, body)
+		}
+	}
+
+	if got := rec.Header().Get("Content-Type"); !strings.HasPrefix(got, "text/plain") {
+		t.Errorf("content-type = %q, want text/plain prefix", got)
+	}
+}
+
+func TestRegistry_LabelsByStatus(t *testing.T) {
+	t.Parallel()
+
+	r := New()
+	r.Observe("/query", "2xx", time.Millisecond)
+	r.Observe("/query", "5xx", time.Millisecond)
+	r.Observe("/write", "2xx", time.Millisecond)
+
+	rec := httptest.NewRecorder()
+	r.Handler().ServeHTTP(rec, httptest.NewRequest(http.MethodGet, "/metrics", nil))
+	body := rec.Body.String()
+
+	for _, want := range []string{
+		`brain_query_duration_seconds_count{path="/query",status="2xx"} 1`,
+		`brain_query_duration_seconds_count{path="/query",status="5xx"} 1`,
+		`brain_query_duration_seconds_count{path="/write",status="2xx"} 1`,
+	} {
+		if !strings.Contains(body, want) {
+			t.Errorf("missing %q in body:\n%s", want, body)
+		}
+	}
+}
+
+func TestMiddleware_RecordsTiming(t *testing.T) {
+	t.Parallel()
+
+	r := New()
+	handler := r.Middleware(http.HandlerFunc(func(w http.ResponseWriter, _ *http.Request) {
+		time.Sleep(2 * time.Millisecond)
+		w.WriteHeader(http.StatusOK)
+		_, _ = io.WriteString(w, "ok")
+	}))
+
+	srv := httptest.NewServer(handler)
+	defer srv.Close()
+
+	resp, err := http.Get(srv.URL + "/query")
+	if err != nil {
+		t.Fatalf("get: %v", err)
+	}
+	_ = resp.Body.Close()
+
+	if resp.StatusCode != http.StatusOK {
+		t.Fatalf("status %d, want 200", resp.StatusCode)
+	}
+
+	// Exposition should now include /query.
+	rec := httptest.NewRecorder()
+	r.Handler().ServeHTTP(rec, httptest.NewRequest(http.MethodGet, "/metrics", nil))
+	body := rec.Body.String()
+	if !strings.Contains(body, `path="/query"`) {
+		t.Errorf("expected /query series, got body:\n%s", body)
+	}
+	if !strings.Contains(body, `status="2xx"`) {
+		t.Errorf("expected 2xx status class, got body:\n%s", body)
+	}
+}
+
+func TestStatusRecorder_DefaultsTo200(t *testing.T) {
+	t.Parallel()
+
+	r := New()
+	handler := r.Middleware(http.HandlerFunc(func(w http.ResponseWriter, _ *http.Request) {
+		_, _ = w.Write([]byte("hello"))
+	}))
+
+	rec := httptest.NewRecorder()
+	handler.ServeHTTP(rec, httptest.NewRequest(http.MethodGet, "/x", nil))
+
+	if rec.Code != http.StatusOK {
+		t.Errorf("code %d, want 200", rec.Code)
+	}
+}