Salesforce is not going to support the non-Chromium of Microsoft's Edge browser starting on December 31, 2020, as per this article:
Salesforce supports the latest stable version of the Chromium and non-Chromium versions of Microsoft Edge for Salesforce Classic and Lightning Experience. Salesforce supports Microsoft Edge Chromium only on Windows.
Maybe you are using the non-Chromium version. Either way, when you open different pages on Salesforce and other services the browser usually sends the session cookies with the request so the server can maintain your session active. If you are being disconnected when you open a new tab, maybe it is a browser setting or bug that is not carrying the cookies.
I would strongly advise to change browsers. Move to Firefox, Google Chrome, Brave or any other Chromium-based browser (since it is the foundation for Chrome, and Salesforce fully supports it).