The login page for bbPress is the same as the WordPress login page. If you are logged into one you are logged into the other.
The individuals can have either the same or different roles for each. The default is to give users the same role for both wordpress and bbpress and to determine what a given role can access in each from the settings. The main exception to this is the bbpress keymaster role which normally needs to be given to the same person as has the administrator wordpress role in order to get the two to work together properly.
without taking a look at a forum, I would say the basics of a forum, Notification system, unread replys, quotes, badges, good Moderation tools, even the bbpress site get spammed daily
I don’t mind a basic forum. if it has most of the basic features needed on most forum. but adding features using plugins will not work, most of the plugins have stopped getting updated,
Sitepoint uses Discourse namely because they are a dedicated ruby house. Unless you plan on moving to ruby or are willing to maintain two completely different technology stacks I highly discourage you from using Discourse. I would recommend a PHP forum since your existing infrastructure and knowledge base can be shared between both the main site and forum. The modern PHP forum that comes to mind is Vanilla. There is also a WordPress integration available. The integration includes single sign on as you desire.
I seem to remember seeing a script for linking WordPress and phpBB together many years ago but I can’t remember what it is called or whether it still exists.