As mentioned the team is aware of the login issues with Error 10010 that started earlier today. We have discovered the cause and are now testing a fix so we can hopefully have this resolved shortly. We will continue to keep you updated!
Until then, there is a work around that you’re welcome to try until the fix is deployed.
Go to your Steam settings → Beta participation under Account tab → change Beta participation to Steam Beta Update
We super appreciate your patience and understanding with this!
None of the solutions mentioned worked for me. This should only be a temporary fix, but I managed to solve it by disconecting from ethernet and entering the game with my moblie hotspot, once inside swap again.