Upgraded to PHP 7.1 - GD or ImageMagick is required
You'll need to contact your hosting provider. There are any number of ways that this "PHP switching" can be implemented, but typically each major PHP version has its own separate modules/config files that tell it which modules to use.

So the fact that ImageMagick is installed on the server doesn't mean that it's globally available to every PHP version that's running. So, contact your hosting provider.

Also, I feel obligated to mention that boutique hosting environments can be a source of issues like this, so I try to avoid them, as per: How Agencies &amp; Freelancers Should Do Web Hosting