First, check whether you actually have PHP 7.3 installed. Ubuntu / Kubuntu 18.04 comes with PHP 7.2 by default, so the package name would be
php7.2-mysql. In case you installed PHP 7.3 from a PPA or some other repository, you might want to check the name of the package in that repo (though there's a good chance that the package's called
Secondly, the package
php7.2-mysql contains the
mysqli functions, among others. You might say, the package contains all bundled PHP extensions for working with MySQL, and there are several. Just because the (very) old style
mysql_ functions were removed doesn't mean that the name of the package changed.
Thirdly, after you installed a new package with PHP extensions, you need to restart the services in question so they "know about" the new functionality. At least the webserver (Apache, NGINX, ...) needs to be restarted. If you're using a separate PHP service like PHP-FPM, you need to restart that, too. The details depend on how you set up your server.