I'm getting exactly the same issue since upgrading to Sonoma 14.2.1 on a M1 Mac mini. I observe YouTube constantly logging me out (sometimes within an hour of a login) and also news.bbc.co.uk losing cookies and asking me to accept cookie preferences again.
Did you file a bug report ? If so what is the reference number and I will add my views to it.
Ian_Dodd
Users receive reputation points by contributing quality content to the forums.
Posts include post and replies published on the forums.
Post authors can mark replies as Accepted to indicate successful solutions.
Apple Developer Forums admins can mark replies as Apple Recommended to indicate an approved solution