We've no phone number verification implemented. You'd need to develop something to utilize an SMS service to send them a text, but that'd only work for cell phones. For land lines I've no idea other that manually calling them. There are no plans at this time to develop and implement something like this, sorry.

Looks like it's just an HTTP request. Yes, that's doable. Ideally you'd extend existing field validation with that so any field can have a phone number validation rule. CB Query Field extends field validation with query validation so that's probably a good place to start.

I think the issue would be from the delay of the code being verified. Field validation would want it validated basically instantly and there's no feature to pause registration. It could be better to allow them to register, but mark them as not approved until the phone number is verified.

You'd use cURL or CBs built in Guzzle library for the HTTP request. You'll need to review CB Query Field to see how it's adding new validation. Specifically its CBfield_queryvalidate class and its XML tag fieldsparams. The validation works on any fieldtype so basically you'd create a text field and turn on your new validation parameter so it'll send the fields value through the HTTP request to validate it as a phone number, but again I'm not sure if this will work as it sends an SMS with a code the user needs to input to further validate it so some other solution will likely be needed. Whether that reloads the registration page by erroring it and telling them to input the code is up to you.