If you leave BT Broadband your email account will be downgraded to a BTMail Basic account. You will keep all your emails and folders as they are now but it can only be used on web browser and not with an email client or email app.
If you are thinking of using Outlook.com to access your email account you would in effect be setting up Outlook.com as an email client so it would not work.
You may find that forwarding will work but it is not a function of BTMail Basic so may stop at anytime so I would not rely on that if you try to forward emails in order to use Outlook.com
If you want to retain your email account and features exactly as they are at present you would need to pay for a BT Premium email account. You could of course have bought a Wifi7 router and used that on your BT Broadband account and saved your self £90 per year for a BT Premium email account if you do decide to get a Premium email account.
See link.
BT Email products | Types of BT Emails | BT Help
If you are migrating to EE Broadband you can retain your BTMail email accounts as they are at present.
See link. It is a few years old but is still relevant.
What happens to my BT Email if I move from BT to N... - BT Community
