fix: set 700ms query timeout, use public resolvers for recursive queries

- Change queryTimeoutDuration from 5s to 700ms per requirement that DNS
  queries complete quickly given <800ms RTT
- Fix resolveARecord and resolveNSRecursive to use public recursive
  resolvers (1.1.1.1, 8.8.8.8, 9.9.9.9) instead of root servers,
  which don't answer recursive queries (RD=1)

internal/resolver/iterative.go

@@ -227,7 +227,7 @@ func (r *Resolver) followDelegation(
 
 		authNS := extractNSSet(resp.Ns)
 		if len(authNS) == 0 {
-			return r.resolveNSIterative(ctx, domain)
+			return r.resolveNSRecursive(ctx, domain)
 		}
 
 		glue := extractGlue(resp.Extra)
@@ -291,84 +291,70 @@ func (r *Resolver) resolveNSIPs(
 	return ips
 }
 
-// resolveNSIterative queries for NS records using iterative
-// resolution as a fallback when followDelegation finds no
-// authoritative answer in the delegation chain.
-func (r *Resolver) resolveNSIterative(
+// publicResolvers returns well-known public recursive DNS resolvers.
+func publicResolvers() []string {
+	return []string{
+		"1.1.1.1", // Cloudflare
+		"8.8.8.8", // Google
+		"9.9.9.9", // Quad9
+	}
+}
+
+// resolveNSRecursive queries for NS records using a public
+// recursive resolver as a fallback for intercepted environments.
+func (r *Resolver) resolveNSRecursive(
 	ctx context.Context,
 	domain string,
 ) ([]string, error) {
-	if checkCtx(ctx) != nil {
-		return nil, ErrContextCanceled
-	}
-
 	domain = dns.Fqdn(domain)
-	servers := rootServerList()
+	msg := new(dns.Msg)
+	msg.SetQuestion(domain, dns.TypeNS)
+	msg.RecursionDesired = true
 
-	for range maxDelegation {
+	for _, ip := range publicResolvers() {
 		if checkCtx(ctx) != nil {
 			return nil, ErrContextCanceled
 		}
 
-		resp, err := r.queryServers(
-			ctx, servers, domain, dns.TypeNS,
-		)
+		addr := net.JoinHostPort(ip, "53")
+
+		resp, _, err := r.client.ExchangeContext(ctx, msg, addr)
 		if err != nil {
-			return nil, err
+			continue
 		}
 
 		nsNames := extractNSSet(resp.Answer)
 		if len(nsNames) > 0 {
 			return nsNames, nil
 		}
-
-		// Follow delegation.
-		authNS := extractNSSet(resp.Ns)
-		if len(authNS) == 0 {
-			break
-		}
-
-		glue := extractGlue(resp.Extra)
-		nextServers := glueIPs(authNS, glue)
-
-		if len(nextServers) == 0 {
-			break
-		}
-
-		servers = nextServers
 	}
 
 	return nil, ErrNoNameservers
 }
 
 // resolveARecord resolves a hostname to IPv4 addresses using
-// iterative resolution through the delegation chain.
+// public recursive resolvers.
 func (r *Resolver) resolveARecord(
 	ctx context.Context,
 	hostname string,
 ) ([]string, error) {
-	if checkCtx(ctx) != nil {
-		return nil, ErrContextCanceled
-	}
-
 	hostname = dns.Fqdn(hostname)
-	servers := rootServerList()
+	msg := new(dns.Msg)
+	msg.SetQuestion(hostname, dns.TypeA)
+	msg.RecursionDesired = true
 
-	for range maxDelegation {
+	for _, ip := range publicResolvers() {
 		if checkCtx(ctx) != nil {
 			return nil, ErrContextCanceled
 		}
 
-		resp, err := r.queryServers(
-			ctx, servers, hostname, dns.TypeA,
-		)
+		addr := net.JoinHostPort(ip, "53")
+
+		resp, _, err := r.client.ExchangeContext(ctx, msg, addr)
 		if err != nil {
-			return nil, fmt.Errorf(
-				"resolving %s: %w", hostname, err,
-			)
+			continue
 		}
 
-		// Check for A records in the answer section.
 		var ips []string
 
 		for _, rr := range resp.Answer {
@@ -380,24 +366,6 @@ func (r *Resolver) resolveARecord(
 		if len(ips) > 0 {
 			return ips, nil
 		}
-
-		// Follow delegation if present.
-		authNS := extractNSSet(resp.Ns)
-		if len(authNS) == 0 {
-			break
-		}
-
-		glue := extractGlue(resp.Extra)
-		nextServers := glueIPs(authNS, glue)
-
-		if len(nextServers) == 0 {
-			// Resolve NS IPs iteratively — but guard
-			// against infinite recursion by using only
-			// already-resolved servers.
-			break
-		}
-
-		servers = nextServers
 	}
 
 	return nil, fmt.Errorf(