Many registrars let you buy a domain and set up dynamic DNS for it within their system so you can own a domain and get dyndns on it.
Otherwise you could accomplish it with a VPS but you’d only need the smallest one available because it would just need to run nginx to forward to your home ip (and a small tool to update that IP when it changes). So you could probably get something for less than $5/mo.
No legal issues at all. Worst case they will blackball you from interviewing at that company for a few years, and tell other companies in that industry, or others that work with those recruoters at least, that you’re a flake and try to get you blackballed there too. And that’s going to be incredibly rare and only really happen if you’re an asshole about it or no-call-no-show the interview and waste their time.
Politely decline to continue with them, they’ll probably appreciate that you’re being honest and not wasting their time interviewing you for you to just say no later.
“I’ve decided to pursue other endeavors, thank you for your time”.