cURL is a required PHP library. Checking, it is not actually listed as a requirement (https://toolset.com/toolset-requirements/), but I suspect that it is because it is almost universally available and the expectation is that it would be.
I don't have any details of your site, could you provide the debug info (hidden link).
It seems likely that your server is not configured with cURL, and you may need to ask your host to add it, but let me see the server configuration for your site.
Here's the debug information. How do I send you the server information? Can I just send you the IP address, or is there a specific set of settings that you need to see?