No need to worry - see how it works out. You have held down the job for a month and that is good.

If they don't progess you in the next few weeks you will have a valid reason to start looking for another position.

No need to quit until you found something else surely.

Do you have regular meetings with your boss? Can you ask for feedback? Do they have any misgivings about you? Might as well find out, though of course you risk not liking what you hear.

It is good for HR people to do a little menial work - gives them insight into how most of the workforce lives. Watch, listen, learn, move on if something better comes up.