Help needed with bathroom faucet drip repair

Hi all,
Trying to do some very basic bathroom faucet repair. The classic dripping faucet. I'm slightly above rookie level when it comes to plumbing stuff. The internet showed me enough to take off the handle in the hopes of getting at the cartridge.
I presume that I need to take off this nut in order to get at the cartridge. However, the nut is so tight, I can't budge it. Or at least, I'm worried something bad is going to happen if I put any more elbow grease into it. I've tried hard enough that the whole faucet began to shift in place.
Is there a reasonable way to loosen this, or should I just be considering a new faucet at this point?
Thanks in advance!

I hope you managed to sort it out. I had this problem and had to get a socket and a metre long extension pole to budge it after applying a heat gun and loads of wd40. I must admit I nearly gave up on it as I was worried about snapping it.

I ran into the same stuck nut problem on my own faucet. Soaking it with penetrating oil overnight and then carefully using a heat gun finally broke it free. If the fixture is truly seized and you are worried about snapping it, I found a reliable local plumber through [gas] https://www.pm247.co.uk/ and they came out same day to handle the replacement quickly without any damage.

I had a similar dripping faucet before, and in my case the problem was a worn washer or cartridge inside the handle. I found discussions like spin king useful for figuring out which part usually fails first. I’d start by shutting off the water and checking the cartridge, seals, and O-rings for wear.