Who owns the site when it's done?
You do. Completely. Domain registered to you, files delivered, hosting set up and managed for you in an account created for your business. If you ever leave, that account goes with you, intact. I keep zero hostages.
What does hosting really cost?
Sites like these run on modern edge hosting that's free at this scale. You pay for your domain (about $10 to $15 a year). That's typically it.
I already have a Wix/Squarespace site.
I rebuild it cleaner and faster, point your domain at the new one, and you cancel the subscription. After that, your only required running cost is your domain, about $10 to $15 a year. A care plan is optional.
What if I need changes later?
Small edits are quick one-off jobs, or the Care plan covers them monthly. Either way it's days, not support tickets.