If your new Microsoft Edge is automatically running on Startup, then its a known issue acknowledged and is being investigated by Microsoft.
Unless you manually add a new Microsoft Edge shortcut to the startup folder, like other browsers, new Edge won’t run automatically on startup.
However, Windows 10 can does this if you’ve enabled sign-in options setting “automatically save my restorable apps when I sign out and restart them after I sign in.
Recently Microsoft Edge Canary got the ability to run PWAs on Startup, if you’ve configured Edge for that, then also new Edge browser will open the PWA when your sign into Windows.
Other than these, if you’re facing the issue, Microsoft wants you to send diagnostic data through the feedback tool built-in to the browser.
We’ve heard from our community that some versions of Microsoft Edge are automatically launching whenever users start their PCs and log into Windows, regardless of their selection in edge://settings/onStartup. It’s currently unknown whether there are any accompanying behavioral changes with this bug.