Trying to understand my 1980s house bathroom wiring.

A little background….My house was built in the mid 80s, and judging by some weird decisions in this house, I’m pretty sure it was built mostly DIY by one person, I’m a woodworker, and a decent handyman, basic electrical and plumbing knowledge, but I’m struggling with understanding what I can and can’t do electrical wise.

I want to add an extra outlet in my bathroom to plug in a new LED mirror. It has hardwiring option, but I really don’t want to do that. I would like a hidden recessed outlet behind the mirror if possible. The 15 amp circuit (22) the bathroom is on right now seems to power a lot of random bedroom lights, bathroom light switch to a light fixture, switch for a small overhead exhaust fan, and a GFCI outlet. The one and only outlet in the bathroom.

What is my best course of action to add another simple outlet behind the mirror?

Can I piggyback off of the light fixture wire which would be the least invasive or maybe from the GFCI outlet? I’m just not sure how to assess my electrical situation to see if adding another outlet is even feasible. Seems like a relatively simple task…but maybe not.