Answer
Page Designer's own save action is driven by the CUSTOM_OBJECTS_ADMIN permission set — grant that specifically if you just need Page Designer access. Be aware CUSTOM_OBJECTS_ADMIN is part of the broader FND_ADMIN permission set's own grant structure, and granting the full FND_ADMIN set (rather than just CUSTOM_OBJECTS_ADMIN on its own) effectively makes that user a full application administrator with access to Solution Manager — grant the narrower CUSTOM_OBJECTS_ADMIN specifically if that broader access isn't actually needed.