healthcheck: answer 503 when the last round of DNS checks reached no root server (closes #302)

The health check answered ok while every DNS lookup failed, as on a
network that intercepts DNS queries. A lookup whose root servers give no
usable reply now fails with ErrNoRootServerAnswered. At the end of each
round of DNS checks the watcher records whether every lookup failed with
it or with ErrIntercepted; the health check then gives status error, and
/.well-known/healthcheck and /health answer 503. Until the first round
finishes it stays ok.

The health check now depends on the watcher, so fx builds the watcher
first: its first round starts before the HTTP server listens, and the
server tests' fx graph includes it. NewWithRootServers lets tests start
a resolver's walks at real servers that are not root servers.

Model: opus-5-5

internal/healthcheck/healthcheck.go

@@ -11,6 +11,13 @@ import (
 	"sneak.berlin/go/dnswatcher/internal/config"
 	"sneak.berlin/go/dnswatcher/internal/globals"
 	"sneak.berlin/go/dnswatcher/internal/logger"
+	"sneak.berlin/go/dnswatcher/internal/watcher"
+)
+
+// Values of Response.Status.
+const (
+	StatusOK    = "ok"
+	StatusError = "error"
 )
 
 // Params contains dependencies for Healthcheck.
@@ -20,6 +27,7 @@ type Params struct {
 	Globals *globals.Globals
 	Config  *config.Config
 	Logger  *logger.Logger
+	Watcher *watcher.Watcher
 }
 
 // Healthcheck provides health status information.
@@ -61,10 +69,17 @@ func New(
 	return healthcheck, nil
 }
 
-// Check returns the current health status.
+// Check returns the current health status. Status is StatusError when
+// the watcher's most recent round of DNS checks could not reach the DNS
+// (see watcher.Watcher.DNSUnreachable), and StatusOK otherwise.
 func (h *Healthcheck) Check() *Response {
+	status := StatusOK
+	if h.params.Watcher.DNSUnreachable() {
+		status = StatusError
+	}
+
 	return &Response{
-		Status:        "ok",
+		Status:        status,
 		Now:           time.Now().UTC().Format(time.RFC3339Nano),
 		UptimeSeconds: int64(h.uptime().Seconds()),
 		UptimeHuman:   h.uptime().String(),