My system check regularly whether their domain has pointed to target.mydomain.com
Now, I am stuck in step 3. My question is, does Cloudflare or any other 3rd party offer API that allow me to check a domain’s target / where the domain point to?
Unless I misunderstand what you are asking, dig or nslookup can do what you are looking for, provided your setup instructions tell your customers to ensure the hostname is in their DNS control panel.
If you are telling your customers to use an hostname, then you could ask your customers to create a scoped API token so you can look at their settings.
You could also make a HTTP request to their hostname for an uncachable URL. As you control the origin you will see the request coming in to your origin which would verify that the requests are going to the correct place.