This topic helped me backup my keys to another MS Authenticator app on a different phone.
In addition I was also able to extract the keys and export them to Aegis Authenticator app using this guide:
https://gist.github.com/chowder/2ead734d60d84d4d15034fcce81aaaf9
This required a rooted android emulator with a play store, but that is the only way that I know off to export keys to a non Microsoft app.
Additionally Aegis can also import Google Authenticator QR codes which most Authenticator apps cannot read. And it can even import Authenticator QR codes from an image file, so you don't need a camera and can use a screenshot image instead. Aegis exports standard QR codes that all Authenticator apps work with.
The reason I exported them is so I no longer have to use Google or Microsoft apps that force users to stay in their ecosystem. I exported some codes to a secure pin protected airgapped hardware authenticator as a secure backup in case my phone breaks or gets lost.
Remember: 2 factor increases your chance of losing access to your account. Always backup your second factor or add an additional alternative second factor.