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/resolver/iterative.go

@@ -293,7 +293,8 @@ func shuffled(
 // place. Otherwise a server that times out, refuses or gives a reply
 // that is not usable is passed over for the next. When every server
 // refused, the error says so, and when they are the root servers it is
-// ErrIntercepted.
+// ErrIntercepted. When the root servers gave no usable reply otherwise,
+// it is ErrNoRootServerAnswered.
 func (r *Resolver) queryServers(
 	ctx context.Context,
 	servers []string,
@@ -352,6 +353,10 @@ func (r *Resolver) queryServers(
 		)
 	}
 
+	if zone == "." {
+		return nil, fmt.Errorf("%w: %w", ErrNoRootServerAnswered, lastErr)
+	}
+
 	return nil, fmt.Errorf("all servers failed: %w", lastErr)
 }
 
@@ -528,7 +533,7 @@ func (r *Resolver) resolveNSIterative(
 	}
 
 	domain = dns.Fqdn(domain)
-	servers := rootServerList()
+	servers := r.rootServers
 	zone := "."
 
 	for range maxDelegation {
@@ -592,7 +597,7 @@ func (r *Resolver) resolveARecord(
 	}
 
 	hostname = dns.Fqdn(hostname)
-	servers := rootServerList()
+	servers := r.rootServers
 	zone := "."
 
 	var withoutAddresses []string
@@ -652,7 +657,7 @@ func (r *Resolver) FindAuthoritativeNameservers(
 	ctx context.Context,
 	domain string,
 ) ([]string, error) {
-	return r.findAuthoritativeNameservers(ctx, domain, rootServerList())
+	return r.findAuthoritativeNameservers(ctx, domain, r.rootServers)
 }
 
 // findAuthoritativeNameservers is FindAuthoritativeNameservers with each
@@ -1127,7 +1132,7 @@ func (r *Resolver) LookupNS(
 	}
 
 	return r.followDelegation(
-		ctx, dns.Fqdn(strings.ToLower(domain)), ".", nil, rootServerList(),
+		ctx, dns.Fqdn(strings.ToLower(domain)), ".", nil, r.rootServers,
 	)
 }