Unique logins and private content

Can anyone advise please on the best way (plugin or theme editing) on how to implement private category content/listings for multiple groups.

A client has asked that they can add in new categories of posts aimed at a specific customer, that only they can see after logging in, like this:

1. Customer logs in .
2. They have a profile page, showing account info they’ve been emailed.
3. They are redirected to a specific category of posts that their account is assigned to.
This shows an archive/category page (ideally with a search only within their specific category.)

For each customer category, multiple users (or groups) can be assigned to each category, so that a Company can have several staff with access.

Ideally, I’m not looking for a new theme-based solution but rather something that can be done via the functions.php, page templates or with a plugin.