healthcheck: answer 503 when no root server gave a usable reply in the last round of DNS checks (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 that shutdown did not cut short, 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 starts the watcher
before the HTTP server and stops the server first. 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(),