feat(library): remote browse status + save/materialize API (§Phase2-3)

Search results now report whether a hit is already saved (in_library,
track_id, availability). New RemoteLibraryService backs POST
/tracks/remote (idempotent placeholder save) and POST
/tracks/{id}/materialize (on-demand fetch via a new materialize_track
arq task, reusing in-flight jobs).

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

app/api/v1/search.py

@@ -18,6 +18,7 @@ router = APIRouter(prefix="/search", tags=["search"])
 async def search(
     _: CurrentUser,
     registry: SourceRegistryDep,
+    track_repo: TrackRepoDep,
     q: str = Query(min_length=1),
     limit: int = Query(20, ge=1, le=50),
 ) -> ExternalSearchResponse:
@@ -25,7 +26,9 @@ async def search(
 
     A source that is down contributes nothing rather than failing the whole
     request (graceful degradation); only available sources are reported as
-    searched."""
+    searched. Each hit is checked against the library by ``(source,
+    source_id)`` so the UI can show "Saved"/"Play" instead of "Save to
+    library" without a separate round-trip (remote browse, plan: Model C)."""
     results: list[ExternalSearchResultOut] = []
     searched: list[str] = []
     for backend in registry.searchables():
@@ -33,7 +36,9 @@ async def search(
             continue
         searched.append(backend.name)
         hits = await backend.search(q, limit=limit)
-        results.extend(ExternalSearchResultOut.from_entity(h) for h in hits)
+        for h in hits:
+            existing = await track_repo.get_by_source(h.source, h.source_id)
+            results.append(ExternalSearchResultOut.from_entity(h, existing=existing))
     return ExternalSearchResponse(results=results, searched_sources=searched)