php -m
should list the modules. Have you manually found the zip.so
Sometimes it dosnt have to be loaded in the Php.ini if it’s compiled, it’s automatic. You might be double loading it.
Now another question is if the other sites are working, why isn’t this one.
Did you Chown/permission the WordPress plugins directory?
Maybe another plugin is interfering. Sometimes bad programming from 3rd party plugins messes up the SQL. Some occasions you have to reset the WordPress plugins folder.
https://wordpress.org/support/topic/how-do-i-reset-a-pluging-using-ftp
I would check the owner/permissions manually, deactivate all your plugins and try BPS activation. If that dosnt work. Then do a plugins folder reset. Also check your SQL tables.