Per the title, where is the logout button?
All the existing questions I can find refer to the previous design of the site, where hovering over your name in the top bar brought up a menu.
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For users that are more visual oriented, here is an animated gif:
As you can see, after clicking logout you see the logout page showing the domains you will also be logged out off.
Mark the checkbox if you want to clear your login session on all devices.
Pressing the log out button completes the logout process.
Click any other link or page to abandon the log out process or click the cancel link.
Click on the Stack Exchange logo on the top-right corner. You'll see a
log out link there next to the site you are logged in.