PHP handler cannot be changed when NGINX service is stopped or not installed.
In Plesk, in Domains > example.com > PHP Settings the checkbox PHP support is disabled and grayed-out with the following message:
PHP support cannot be enabled because current hosting configuration does not include any PHP versions available for this domain.
Unable to retrieve PHP settings because this handler is corrupted.
Current PHP version is shown in Domains > example.com under PHP Settings:
Plesk bug with ID #PPPM-9016 fixed in:
For Plesk Onyx 17.8, install the latest Plesk micro-updates.
For Plesk Onyx 17.0 and 17.5, consider upgrading to the latest Plesk version.