You want to used Tracked, not Everything. Tracked shows any new posts of boards or threads you are tracking. You can change those being tracked by clicking the bell.
You cannot hide the message count on “Everything”, but you can minimize the COMMUNITY section in the sidebar. You can also click the hamburger to hide the whole sidebar.
The Suggested Topics below every topic can only be disabled site-wide by the admins.
I tried to combine Tracked and Latest, but clicking on Latest undid Tracked. Then, somehow, I found I was looking at a screen that had both! Not to look a gift horse in the mouse, I created another bookmark in my browser, pointing to: