Add GitLab Next functionality to the new User menu

The following discussion from !110222 (merged) should be addressed:

• @ohoral started a discussion: (+1 comment)

  @thutterer One thing I've noticed when working on the User menu, there is Switch to GitLab Next item which I suppose should be either on the help menu or the user menu. @nickbrandt WDYT, where it belongs? If it belongs to the help menu, it can be a next follow-up, if it belongs to te user menu, I'll add it in the scope of the user menu MR.

  Screenshot_2023-02-02_at_14.15.38

After some discussion we decided to add it to the new User menu for both mobile and desktop.