test(plex): cover create write-through + the 409->nameTaken mapping (F-F)

Backend: create-collection happy path (write-through + editable) and the
create resync-failure 422 (honest reconcile detail), mirroring the rename/remove
tests. Frontend: extract notifyCollectionEditError (the 409->nameTaken vs
generic-fallback mapping that was inline in the New-collection create()) and
unit-test it; wire create() through it.

backend/tests/test_plex_collections_filter.py

@@ -303,6 +303,54 @@ def test_remove_item_writes_through_to_plex(db, monkeypatch):
         app.dependency_overrides.clear()
 
 
+def _resync_create(db, plex, lib, rk):
+    """Create-path resync stub: the new rating_key has no local row yet, so materialize it."""
+    col = PlexCollection(rating_key=rk, library_id=lib.id, title="Fresh Coll", child_count=1)
+    db.add(col)
+    db.flush()
+    return col
+
+
+def test_create_writes_through_to_plex(db, monkeypatch):
+    _lib, user = _seed_editable(db)
+    stub = _CollStub()
+    client = _admin_client(db, user, monkeypatch, stub, resync=_resync_create)
+    try:
+        r = client.post(
+            "/api/plex/collections",
+            json={"library": "1", "title": "Fresh Coll", "item_rating_key": "m1"},
+        )
+        assert r.status_code == 200, r.text
+        assert "create_collection" in stub.calls
+        body = r.json()
+        assert body["id"] == "NEW"  # the stub's new ratingKey
+        assert body["editable"] is True  # create marks the new collection editable
+    finally:
+        app.dependency_overrides.clear()
+
+
+def test_create_resync_failure_is_422(db, monkeypatch):
+    # The collection was created in Plex (wrote=True) but the follow-up resync read failed → 422 with
+    # the honest "reconcile on the next sync" detail, not a false "write failed".
+    _lib, user = _seed_editable(db)
+    stub = _CollStub()
+
+    def _boom(db_, plex, lib_, rk):
+        raise PlexError("read failed")
+
+    client = _admin_client(db, user, monkeypatch, stub, resync=_boom)
+    try:
+        r = client.post(
+            "/api/plex/collections",
+            json={"library": "1", "title": "Fresh Coll", "item_rating_key": "m1"},
+        )
+        assert r.status_code == 422, r.text
+        assert "reconcile" in r.json()["detail"].lower()
+        assert "create_collection" in stub.calls
+    finally:
+        app.dependency_overrides.clear()
+
+
 def test_mutation_failure_returns_422_write_failed(db, monkeypatch):
     # The Plex mutation itself raised → the write never landed → 422 "Plex write failed", and resync
     # is never reached (stub.calls holds only the mutating call).