Note that modern web browsers do not define a session end as "when you close your browser" unless you hunt for and enable settings to make them do that. Session

Note that modern web browsers do not define a session end as "when you close your browser" unless you hunt for and enable settings to make them do that. Session cookies will happily survive a browser restart by default, because browser makers know that most users don't consider closing their browser to be ending any kind of session.