I am not sure if I looking in the right place in Capture One...
Auto None is fine. The preference settings may or may not be what you want, you need to experiment with those and also manually trigger Sync/Load metadata in the metadata tool. and look for changes in PM+ and in C1. It is important tpo make sure that one application writes metadata where the other application will look for it. Some metadata may exist multiple places, your preferences tells Capture One where to look. I don't remember what Capture One does if the preferred location is empty. Capture One keeps its own set of metadata in the database. Auto set to None, means you need to manually trigger a write ("sync" in Capture One lingo) from database to sidecar. Use Sync Metadata in the metadata tool.
You should also know that exchanging color labels depends on common color coding in both application. Experiment with some other metadata field first, star rating for example. When that works, you can investigate color labels.