It is unacceptable and you were only very slightly in the wrong imo (for being slightly late but we’re all human, bar some of the superhuman PP apparently).
if this was me and my normal nail tech she’d be fine, we’d assess time once I’d had my builder gel put on and any fancy design may go out the window for plain (probably at my insistence).
I'd be livid if my nail tech treat me like yours did at my appt, it’s an expensive thing to get done regularly and a nice little treat. Not something I would want ruined with a teenager like sulk.