How Do I Hide Tabs Inside Plugin Settings?

It is not possible to guess without having that plugin source code.

In general, you check if plugin protects menu items or tabs with separate user capability or write custom code to exclude selected tab from the page. Some plugins offers filters for that, for some you have to write JavaScript code to change CSS or delete part of HTML from the page according to the current user role, like:

if (current_user_can('some_role')) {
// your code for that role here

}

And put that code to the active theme functions.php file or use it as a ‘must-user’ plugin.

I don’t understand most of what you said. I can give you the plugin if you want to check the code. If you edit the actual plugin, will the custom code get removed once you update the plugin?

Send the plugin to the support [at-sign] role-editor.com
You should not edit actual plugin exactly for this reason – the custom code will be removed once you update the plugin.

@garzilla provided the plugin for the investigation purpose. In case if someone else is interested to find the decision, it is available here:
https://www.role-editor.com/manage-access-to-mymail-email-newsletter-settings-tabs/