Actually your feelings are remotely correct. A key holder must be on duty (being on lunch counts as “on duty” even though they are clocked out). Fun fact: my previous DM had a rule that a supervisor wasn’t allowed to leave the store on their lunch if there wasn’t another on the floor (I got in trouble for sitting outside smoking), but my current DM is ok with supervisors leaving to get food somewhere even if it’s a car ride away. So it might be up to the DM, but my understanding is: if there is no key holder, that can create serious cash handling issues. If a barista is holding keys, that’s a security violation.
That being said, emergencies are grey areas.
You have every right to be frustrated, that’s a lot of nonsense to deal with.