Well, it can’t hurt to cross it off. You don’t need to get a domain from a registrar that offers dynamic DNS, you just need to register a domain (or try another dynamic DNS like the other user suggested) and use a DNS provider that is free and offers an API. I personally use Cloudflare, there are plenty of guides for setting up a dynamic record on CF.

For registering a domain you can use an affordable registrar, I’m a Porkbun customer - for a .com domain it’s like $11 for a year. No need to spend monthly.