You use an ACME client (either explicitly with e.g. certbot or a webserver that has a client Iintegrated like Traefik, Caddy,…) to communicate with an ACME server (the CA, e.g. Let’s encrypt). Your ACME client asks for a certificate with a DNS challenge. It gets a code that you/the client needs to publish as a DNS record. Only then the client talks to your DNS provider and tells them to put a specific TXT record on your domain (or onanual mode: the client prints out the value and you need to put it there manually). After your DNS provider published it, your client tells the server to check the challenge and hand you your certificate.
Your DNS provider in this diagram is just that one small rectangle in the lower left.
Note: There’s nothing stopping your DNS provider to just do all of this, generate a certificate for you and providing you with a button in your account where you can download a certificate with a single click. Also if you are at a webhoster and only host a simple page there, they will probably also provide your with a TLS cert with the click of a single button.
Wouldn’t the authentication API provided by your DNS host be the ACME server?
No, see also this diagram: https://www.digitalberry.fr/wp-content/uploads/2023/02/DNS-challenge-process.png
You use an ACME client (either explicitly with e.g. certbot or a webserver that has a client Iintegrated like Traefik, Caddy,…) to communicate with an ACME server (the CA, e.g. Let’s encrypt). Your ACME client asks for a certificate with a DNS challenge. It gets a code that you/the client needs to publish as a DNS record. Only then the client talks to your DNS provider and tells them to put a specific TXT record on your domain (or onanual mode: the client prints out the value and you need to put it there manually). After your DNS provider published it, your client tells the server to check the challenge and hand you your certificate.
Your DNS provider in this diagram is just that one small rectangle in the lower left.
Note: There’s nothing stopping your DNS provider to just do all of this, generate a certificate for you and providing you with a button in your account where you can download a certificate with a single click. Also if you are at a webhoster and only host a simple page there, they will probably also provide your with a TLS cert with the click of a single button.