You do not need a static IP address or dynamic DNS if your domain registrar provides a REST API. My current registrar is Porkbun and they have a REST API. I simply have a cron job that regularly checks if my public IP[^1] differs from the domain’s A-record. If it does, it updates the record to match the public IP address.

[^1]: I use Porkbun’s ping endpoint to obtain my public IP.