Usually it's not them remembering you but your browser remembering them, so yeah, the checkbox doesn't do what it claims to do. My browser deletes all cookies when I close it, so none of these checkboxes works here unless I configured an exception.

Fr. I think it's a hidden consent button to collect and store all your data. Like, "sorry, but you ticked the box now we can never forget you."

Definitely not in any Microsoft SSO forms.

"Keep me signed in?" Has never worked lol