Hi,
unfortunately we not have control about phone validation (it comes from HTML5 + Joomla validation).

Anyway you can use a Text field type and add your custom format. see screenshots.

Something like

[0-9 ]+

should allow numbers and spaces

Obviously the validation works, but the message is not clear on what is wrong!

I know, but message comes from Joomla, not Easy Profile, JForm API of Joomla not allow natively to add error messages on client validation.
Keep in mind that Easy Profile extends Joomla user management (not replace), so registration form is the same of Joomla and it uses Joomla validator.

You need to write some javascript function to customize your message.

Or more simple:
- add description in phone field (this will be shown as tip, see screenshot)
- add HTML delimiter after phone field to describe valid format