Need to configure permissions on pages using categories/tags custom field on the page.
For instance, if adding the "team-A" category to the page, give edit access to the group of users which are in "Team A" role.
Need to have simplicity for the users as they give other people access to content which they need to edit. Additionally, the users who are needing to add access to others are not administrators, so they don't have the ability to granularly define permissions via native Sitefinity pages. 

There is no out of the box functionality to consider tags and categories as enforcers of page permissions.

A custom functionality has to be developed via utilizing Sitefinity API to work with pages, tags/categories, permissions, users/roles.
To develop this functionality development experience with C# language will be needed.

In the scenario where a user assigns tags/categories to a page instead of actually changing page permissions the first thing to happen is to intercept any update done to Title and Properties screen of a page


When a user updates tags/categories in Title & properties a code interception has to occur which will allow for API code to run and assign permissions to a page.
Such interception is available by subscribing to a Sitefinity event called IDataEvent Sitefinity Documentation IdataEvent https://www.progress.com/documentation/sitefinity-cms/for-developers-idataevent sample usage and filtering of the event sampled in How to catch the Publish, Unpublish and Save as draft events using API

With this subscription whenever a user assigns saves an update to the Title & properties screen of a page this event will trigger. The next thing is to work with Sitefinity`s APIs to work with pages, tags/categories, permissions.

Pages:
In the IData event there will be access to the page that gets currently processed. Utilize Sitefinity API for pages from Sitefinity Documentation, query pages https://www.progress.com/documentation/sitefinity-cms/for-developers-query-pages to work with page and get the value of the selected tag/category. The value of the tag/category will be needed in determining what permission to assign.

The API method to obtain values from custom fields is via extension method .GetValue. API sample in Sitefinity Documentation, access custom fields with the API https://www.progress.com/documentation/sitefinity-cms/for-developers-access-custom-fields-with-the-api. To access this extension make sure to add reference to :

using Telerik.Sitefinity; 

to the class where values from custom fields are to be obtained.
The values from tags and categories will be Guid values with the ID of a tag/cat. That GUID will need to be processed with tags/categories API to obtain the actual name of the taxon. API samples in Sitefinity Documentation, taxonomies API https://www.progress.com/documentation/sitefinity-cms/for-developers-taxonomies.

The last component is to assign permissions to the page. This is done with permissions API. A complete code sample for breaking the permission inheritance of a page (prerequisite to be able to assign permissions on a page)


available in How to break inheritance and grant permissions to a Role for all the permissions set of a Page programmatically .
To use the snippet pass the ID of the page and the ID of the user role which must be granted permissions. Incorporating Roles API will be needed as well, documentation in Sitefinity Documentation, roles API https://www.progress.com/documentation/sitefinity-cms/for-developers-roles-api.