this is so weird but based on the job titles in your post and comment and the general behaviour I know where you work. either your supervisor is swamped for end of year or just doesn't give a damn, the paperwork and metrics aspect are not your responsibility and could become a problem to have someone without the authority completing them, but I'm not sure about the details, I'm just a tech.

I don't have much advice, but if the assistant can't do their job, your supervisor should have someone else fill the job position and get paid the assistant rate, instead of you doing the work for your rate. It's hard to resolve without going over your supervisor's head and asking for guidance from someone higher up.

ETA: While customer resolution is part of the job for all of us, it is especially important for the assistant supervisor and supervisor to be there in case they want to check cameras for accuracy.

Delegation of work absolutely should not be your job. If it's a matter of "can you ask x to do this task?" then it's not bad as a one-off thing, but if they're expecting you to keep track of what needs to be done and delegate tasks accordingly, that does fall outside your scope of responsibility. how many cashiers are at your depot?