Changing mobile phone, 2FA, and authenticator apps

[Quartz]

At some point I'm going to be changing my mobile phone. I currently use a Lumia 950. Now, I use my phone for 2FA, some via SMS but some - like OCUK - via the authenticator app. As long as I keep my phone number, the SMS authentication will be fine, but I'm worried about the authenticator app issue. Suppose I have the perfect storm of replacing my phone when OCUK demands re-authentication?

I'm probably worrying over nothing, but I'd like to be sure.

 

[Quartz]

Just make sure you have an overlap with both phones available?

If my phone breaks, that may not be possible.

Hmm... I use the Microsoft Authenticator. Are the sites stored against my Microsoft account?

 

[Quartz]

I already have sets of backup codes.