Practically every hosting meets these requirements. You must use PHP at least 7.0 and have the GD or Imagick extension installed. The extension must support WebP format. If you have an error saying that the GD or Imagick library is not installed, but you have it installed then they are probably incorrectly configured and do not have WebP support.
They are required native PHP extensions, used among others by WordPress to generate thumbnails. Your server must also have the modules mod_mime, mod_rewrite and mod_expires enabled.
Your current server configuration can be found in the Server Configuration tab on plugin settings screen.
Note the items marked in red. If the values marked in red do not appear in your case, it means that your server does not meet the technical requirements. Pay attention to the WebP Support value for the GD library and WEBP in the list of supported extensions for the Imagick library.
In a situation where your server does not meet the technical requirements, please contact your server Administrator. We are not able to help you. Please do not contact us about this matter, because this is a server configuration problem, not a plugin.
Also, REST API must be enabled and work without additional restrictions. If you have a problem with it, please contact the Developer who created your website. He should easily find the issue with the REST API not working.