Magento 2 logged in one browser , will open another browser account page support session how?
Each different browser keeps its own set of cookies (which are the technology underlying sessions) - they are not shared between different browsers.
If you really have to do this, you could do something horrible like pass along a query parameter (very insecure!) between pages to act as a session ID, bypassing the actual $_SESSION altogether and managing your own concept of a session. Again, this is not normal and will only lead to headaches/security issues in the future.