When using Microsoft Edge Canary Version 78.0.261.0, my login to outlook.live.com is not persistent after closing and re-opening Edge Canary. I have to login and go through the 2FA rigamarole each time I open Edge canary. I don't have this problem with mainstream Edge or Firefox.
You can also try deleting your user data folder: C:\Users\UserName\AppData\Local\Microsoft\Edge SxS\User Data (replace UserName with your own Windows username) that will do a more thorough clean up. it will delete all of your browser data (bookmarks, passwords etc) But if you're using cloud sync you don't have to worry.
i'm on Version 78.0.262.0 (Official build) canary (64-bit) and don't have that problem. it's possible that the internal database of Microsoft Edge got corrupted so that clean up should fix it.