No problems here too.Does anyone use Microsoft Edge? The Steam website behaves strangely with it. I'm logged out when i start Edge and visit the Steam store.
When i log back in and close Edge, i am logged out again. If i try it a second time, Steam shows the message "There have been too many login failures from your network in a short time period. Please wait and try again later. "
With Firefox it works without problems.
Clean all the cookies for Steam and see if it persists