PHP handlers "served by Apache" options are missing in PHP settings in Plesk

Symptoms

All served by Apache Plesk PHP handlers are missing from the drop-down in Domains > example.com > PHP for any PHP version.

Cause

Proxy Mode is disabled, which turns off Apache and serves the site entirely with nginx. As the result, FPM application served by Apache and FastCGI application served by Apache are disabled.

Resolution

1. Log in to Plesk
2. Go to Domains > example.com > Hosting & DNS > Apache & nginx
3. Enable Proxy Mode
4. Press the OK button