Logout not actually logging out

Hello,
Each time I logout, if I try to log back in I appear as if I didn’t logout (except I don’t have access to the restricted pages, even if i see them reapear in the menu). Instead of login form it returns “Your account” and “logout” links that display the exact same thing when clicked.

I have tried switching the theme to a basic one, turned off plugins and contacted my hosting provider to check if there are issues on the server, but without success. I didn’t find any other solution on this forum – am I doing something wrong?

Thank you!