Hello.
As long as you still keep the old email as an alias it would be fine. But if you plan on deleting the old email as alias, then it’s important that you relink your Microsoft account on the computer to use the new alias before you delete it. Your files and apps will still stay intact because it’s still the same Microsoft account.
This is how you relink.
Go to Settings > Accounts > Your info
Click on Sign in with local user instead. follow the steps and finish the rest.
(If you don't see the "sign in with a local account instead option, click on "Stop signing into Microsoft apps automatically" first, then relaunch this page. )
Restart the computer (Do Not skip)
Go to Settings > Accounts > Your info
Click on Sign in with Microsoft account instead. follow the steps and finish the rest. Sign in with the new alias email.
Restart the computer (Do Not skip)