Do you mean you are editing a field group at Toolset > Custom Fields and are trying to add a field to a field group?
The add field button you mention is the one in the screenshot?
If the button is not working (or it is another add field button, please show me in a screenshot) there would likely be a JavaScript error in the browser console, if you could please check and let me know.
Also, could you please provide your site debug info in your next reply? hidden link
Those many errors are all generated because jQuery is not being loaded on your site, even though it is a core WordPress asset loaded automatically on all WordPress sites.
It seems that something is preventing jQuery from loading on your site.
Perhaps your installation of WordPress is somehow corrupted: you can go to Dashboard > Updates and re-install WordPress.
Or some other code has disabled jQuery.
According to your debug info you only have Toolset plugins installed. If this is correct then it suggests it must be your theme. Please switch theme to twentynineteen and then test again and see if you still have this issue.
We had another report of something similar and so I did some testing and this does in fact appear to be a problem with our plugins.
With the current version of Views if you go to Toolset > Settings and specify that the site is not using Bootstrap you will get errors such as those you report that jQuery is not defined.
I'm escalating this thread and I'll update you when I get feedback from the developers about a fix or workaround.
Could I get access to your site? I want to check the settings, and if needs be take a copy of your site to install locally for further testing.
I will mark your next reply as private so that I can get log-in credentials from you—you may want to create a temporary admin user for me to use that you can later delete. And be sure to have a current backup of your site.