Recovering Facebook Two-Factor Authentication Without Access to Phone

Question

I had two-factor authentication enabled on my Facebook account. My phone fell and broke, making it impossible to interact with the screen. I bought a new phone, but after installing the Facebook app and authenticating with Microsoft Authenticator using the same account, I noticed that the "get code for Facebook" option is not available in the service list. How can I get the code?

I also don't understand if my keys are stored in the cloud.