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/search/engine.go

@@ -20,7 +20,7 @@ type Engine struct {
 	CacheTTL  time.Duration
 	Embedder  Embedder
 	Log       *slog.Logger
-	Degraded  []string // healthz: "search.brave_llm: missing key"
+	Degraded  []string // static: missing keys
 	TavilyCap int
 	Now       func() time.Time
 
@@ -46,6 +46,27 @@ type RunResult struct {
 	Attempted     []string
 }
 
+type readySrc interface {
+	Name() string
+	Ready() bool
+}
+
+// Health is missing keys plus sources that still have no pin.
+func (e *Engine) Health() []string {
+	if e == nil {
+		return nil
+	}
+	out := append([]string(nil), e.Degraded...)
+	for _, s := range e.Sources {
+		r, ok := s.(readySrc)
+		if !ok || r.Ready() {
+			continue
+		}
+		out = append(out, "search."+r.Name()+": unresolved")
+	}
+	return out
+}
+
 func (e *Engine) now() time.Time {
 	if e != nil && e.Now != nil {
 		return e.Now()