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How long did you wait at this point? I just replicated the issue. These warnings are expected since you already have nginx installed and the phpmyadmin Ubuntu package lists apache as a prerequsite.
I noticed that when I went through the process the output paused at this point for about 30 seconds. It is also important that you do not let the installation process auto-configure apache, when prompted you should tab down and choose next without selecting either option.
PHPMyAdmin is not super hard to install from scratch and if you plan to use it without Apache on Ubuntu this might be a good option. Since it’s just a PHP application you should be able to create a new directory on your LEMP web root and download PHPMyAdmin from the official site.
Yet another option (and one I’ve used myself where I didn’t need to do a lot of direct administation of my database) is Adminer. It is similar to PHPMyAdmin but is implemented in just one file so you can drop it anywhere in your web root and browse to it. Log in using your existing MySQL credentials and you can manage your databases.