Serve Prometheus metrics at /metrics behind basic auth (closes #94)

With METRICS_USERNAME and METRICS_PASSWORD both set, the backend
records request metrics through go-http-metrics in a registry of its
own, with Go's runtime and process metrics, and serves them at
GET /metrics behind basic auth; nginx passes /metrics to it. With
neither set there is no such route; one alone, or a METRICS_USERNAME
containing ":", stops the start with an error naming the setting.

Only requests that reach the health check or POST /api/v1/reports are
recorded, as the labels are path and method, which clients could
otherwise make up without end; POST /api/v1/reports is registered by
its full path for that.

Deviation: go get and go mod tidy ran directly; no entrypoint added a Go
dependency yet (issue #45).

Model: opus-5-5

backend/internal/config/config_test.go

@@ -103,6 +103,32 @@ func TestDataDirMaxBytesMustBeANumber(t *testing.T) {
 	requireConfigError(t, "DATA_DIR_MAX_BYTES")
 }
 
+// TestMetricsCredentialsGoTogether: with only one of the two set, the
+// server would quietly serve no metrics, so the start fails, naming
+// both.
+func TestMetricsCredentialsGoTogether(t *testing.T) {
+	for _, set := range []string{"METRICS_USERNAME", "METRICS_PASSWORD"} {
+		t.Run(set, func(t *testing.T) {
+			t.Setenv("METRICS_USERNAME", "")
+			t.Setenv("METRICS_PASSWORD", "")
+			t.Setenv(set, "prometheus")
+
+			requireConfigError(t, "METRICS_USERNAME")
+			requireConfigError(t, "METRICS_PASSWORD")
+		})
+	}
+}
+
+// TestMetricsUsernameMustNotContainColon: basic auth splits the
+// credentials at the first ":", so such a user name would get 401 on
+// every request to /metrics.
+func TestMetricsUsernameMustNotContainColon(t *testing.T) {
+	t.Setenv("METRICS_USERNAME", "prom:etheus")
+	t.Setenv("METRICS_PASSWORD", "secret")
+
+	requireConfigError(t, "METRICS_USERNAME")
+}
+
 // TestCORSAllowedOriginsMustBeOrigins: "*" would let every origin in,
 // and an entry that is not a plain origin would match no page.
 func TestCORSAllowedOriginsMustBeOrigins(t *testing.T) {