On Linux I am rarely if ever compelled to reboot unless I upgrade the kernel and want to use specific features like virtualization. There's just no going back once you get used to this.
[1] I know, I know, why use Edge? Fun fact, Netflix doesn't render at higher than 720p on Firefox/Chrome because of DRM issues.
In short:
1. Run this command as an administrator: reg add hklm\SOFTWARE\Policies\Microsoft\EdgeUpdate /v Allowsxs /t REG_DWORD /d 1
2. Download and reinstall the new Edge.
Note that Microsoft has said that old Edge will stop getting security updates soon, though I don't know what this actually amounts to as the old Edge's engine remains in Windows for application compatibility even when old Edge is nominally removed.
I'd also suggest that you send feedback to Microsoft about any problems you have with new Edge, using the built-in "Send feedback" tool or Windows' Feedback Hub.