I wouldn’t bother with a paid dynamic DNS. Most domain registrars let you change your DNS record with an API call (I know GoDaddy does because I use them.)

Then you just set up a cron job to fetch your IP and then change your DNS record to match. I use a subdomain because my main domain hosts a blog and some other stuff on a VPS, while my jellyfin server is at home.

A good search would be “[registrar name] dynamic DNS script”