Domain and hosting are different
A domain is an address. Hosting serves the page at that address. You need both, plus a valid HTTPS certificate, for a working public website.
Prepare a safe changeover
Keep your old page live. Set up the new destination, verify HTTPS, test every link and update social profiles only after the new address works.
Own Bio Link domain support
Managed domain connection and user subdomain publishing are planned. Today you can download HTML and arrange compatible hosting yourself; Own Bio Link does not configure that hosting for you.