I checked in online for Swiss flight LCY to Zurich and it aske dme for either resident's permit details or visa! UK passport holder with a B permit. I entered those details and all was fine. My wife wasnt asked as she is EU passport holder. Was this an error or require dnow? I saw ETIAS is arriving in 2024, so this has confused me slightly.
Did you book a one way ticket? In that case the answer is obvious, you have to show your right to stay beyond the max. permitted 90 days in any given period of 180 day.
If I understand you correctly you are talking about a process operated by an airline, not any official operated by the authorities. And given that they have to pay a fine (3,000 Euros I think) if they land someone who is later refused entry, they get to decide who they will carry and on what basis.
If you are a resident always present your Swiss passport or Permit to the airline.
If you are neither present your British passport with proof that you are leaving Schengen within 90 days. Could be a return ticket or ticket for onward travel. Or a rdv with Dignatas although that might also require a prepaid air waybill for your mortal bits.