When you are in family tree and click on a link to an URL the click takes you to the sign in page not to the docuement.
Either you were logged out, somehow you were not logged in when tree climbing or the resource you are accessing on that URL needs to doublecheck your login/account. There are some options on FamilySearch that might let you browse Tree profiles but not be logged in.
I was logged in but when it took me to the login page I could not press the back arrow to get back into the tree I was working on. This has been going on for a couple of days, I suggest you try it and see what happens to you. Please let me know. Thanks
I cannot duplicate the issue on Windows 11 Chrome Version 99.0.4844.51 (Official Build) (64-bit) DSL Wifi
You could try the login option to stay signed in for 2 weeks - if you are using a private computer.
I have experienced similar behavior, where FamilySearch keeps logging me out, but not recently.
Whenever I get logged out, then log back in, I will need to make my browser refresh any FamilySearch pages I may have left open.