p3: tavily parse errors degrade; retry DNS on search

A 200 with a bad Tavily body is tavily: error, not an empty success
that would cache for the hour. Upstream clients stay in the source
list if DNS is down at boot and retry the pin on Search; /healthz
lists them as unresolved until a pin lands.

internal/api/api.go

@@ -110,9 +110,11 @@ func (s *Server) healthz(w http.ResponseWriter, _ *http.Request) {
 	if s.SelfIP != nil {
 		out["self_ip"] = s.SelfIP.Status()
 	}
-	if s.Search != nil && len(s.Search.Degraded) > 0 {
-		out["status"] = "degraded"
-		out["search"] = s.Search.Degraded
+	if s.Search != nil {
+		if d := s.Search.Health(); len(d) > 0 {
+			out["status"] = "degraded"
+			out["search"] = d
+		}
 	}
 	_ = json.NewEncoder(w).Encode(out)
 }