To start with, that is a stake nut. You can see on the bottom about 5oclock position the edge of the nut is dented in, that locks it to a keyway on the cv axle shaft. There's not much left of that ofc but it's still holding something in place and not helping. Usually have to grind that off or pry the staked part out using a screwdriver.

I borrow a 3/4" anvil high-flow pneumatic impact wrench for stuck axle nuts. On clean west coast cars I can use my normal impacts but anything with the slightest modicum of rust needs the most torque you can throw at it. Use a high quality black 6pt impact socket to have the highest chances of removal without rounding the nut.

Something else you can do is put a heavy duty breaker bar on it that is longer than your tire, then drive the car backwards/forwards to apply torque. This usually breaks most breaker bars though, unless you get a 3/4 or 1" anvil.

Honestly at this stage I am assuming the end of that CV axle is cooked. I have very little hope that the threads will be usable once it comes off- and seeing as the CV axle holds the wheel bearing together, its not something I would chance. You can get aftermarket cv axles that usually last maybe 50k for under $80 US, which they suck but it is no 500CAD that you probably got quoted for an OE axle.

If that isn't an option you could leave the outboard joint alone and disassemble it from the inside half by removing the knuckle from the car (disconnecting brake caliper, control arms, and the shock/strut) and sliding the axle out of the trans. Most CV axles can disassemble from one or both sides for a boot replacement.

If the nut totally fucks off and you are SOL on the axle, drilling out the axle center in progressively larger holes until the threads are gone and the outer piece falls off might be your best bet.