Update Feb 19, 2022:
This was partially fixed a while ago (i.e., on desktop mode) but just reappeared on all pages of Meta Stack Exchange, specifically (I can't repro on other sites):
I noticed that when I open the Stack Exchange menu on desktop while on the profile page (mine or another user's), it includes my user card, which a) takes some real estate from the drop-down menu, b) messes up with my muscle memory when I try to visit a site, and c) is redundant because it's already there in the top bar.
Actually, it depends on the device / screen resolution. Here are the details:
|Desktop, full window||Any page except profile||The menu looks normal (the way it used to)|
|Desktop, full window||profile page||Extra user card + extra "log out" link|
|Mobile / narrow screen (responsive)||Any page||User card + extra "log out" link|
For desktop, here are the two views side by side:
This bug was likely introduced by this recent fix.
I think the user card should be removed from both the "wide view" (e.g., desktops) and narrow-screen view (e.g., responsive design on mobile phones). But if it's decided that it should be shown on narrow-screen views (for rep and badges), then at least one "log out" link should be removed.
This is how it currently looks on responsive design on mobile (all pages):
Addendum: As zcoop98 pointed out in the comments, the two "log out" links are also shown on the mobile view (not responsive).