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.go

@@ -44,6 +44,15 @@ var (
 	errNotPort = errors.New("must be a port number, 1 to 65535")
 	errNotBool = errors.New("must be true or false")
 	errNotIP   = errors.New("must be an IP address, or empty")
+
+	errMetricsCredentials = errors.New(
+		"METRICS_USERNAME and METRICS_PASSWORD must be set together, " +
+			"or neither",
+	)
+	errMetricsUsernameColon = errors.New(
+		"METRICS_USERNAME must not contain \":\", " +
+			"which basic auth cannot carry in a user name",
+	)
 )
 
 // Params defines the dependencies for Config.
@@ -178,6 +187,18 @@ func (s *Config) check() error {
 		}
 	}
 
+	// The server records and serves metrics only with both set, so
+	// one alone is a mistake that would otherwise go unnoticed.
+	if (s.MetricsUsername == "") != (s.MetricsPassword == "") {
+		return errMetricsCredentials
+	}
+
+	// Basic auth splits the credentials at the first ":", so with one
+	// in the user name every request to /metrics would get 401.
+	if strings.Contains(s.MetricsUsername, ":") {
+		return errMetricsUsernameColon
+	}
+
 	return checkOrigins(s.CORSAllowedOrigins)
 }