I understand how frustrating and concerning this situation must be. Losing access to important accounts like email can be a real headache. Here's what I would suggest doing:
Firstly, let's focus on regaining access to your Hotmail account. Since you've changed phones and can't access the authenticator app, your best bet is to try to reset the authentication method associated with your account. You can usually do this by going through the account recovery process provided by Hotmail. They'll likely ask you to verify your identity through alternative means, such as providing personal information or answering security questions. Once you've verified your identity, you should be able to either deactivate the authenticator app or set it up again with your new phone.
Regarding migrating your emails to a new account, Hotmail doesn't provide a direct feature for this. However, you can manually transfer your emails by forwarding them to your new email address or by using an email client to download them and then upload them to your new account. It's a bit tedious, but it ensures you won't lose any important information.
As for setting up email forwarding without going through second-factor authentication, unfortunately, most email providers, including Hotmail, require authentication for security reasons. However, once you regain access to your account and update your authentication method, you can set up email forwarding as needed.
