This may be a plugin or theme conflict. Please attempt to disable all plugins, and switch to the default Twenty Twenty theme. If the problem goes away, enable them one by one to identify the source of the problem.
If you can install plugins, install Health Check. On the troubleshooting tab, you can click the button to disable all plugins and change the theme for you, while you’re still logged in, without affecting normal visitors to your site.
That did the trick. The problem child plugin is Affiliate Royale. I’ve deactivated it and now the “generate password” button is working.
Now to get AR to fix the plugin.