Switching Phones/2FA App Question

My Samsung S10 is fading fast. Purchasing a new Android phone.

I recently started using Google Authenticator for much of my 2FA needs. 

As I've never done this before, how do I have websites recognize my new Android phone with newly installed Authenticator app?

Does keeping the same number factor into this?

Don't want to get locked out.

All new to me.

Thanks in advance.

Google Authenticator now allows you to sync it to your Google Account so when you get a new phone you can sync it. I don't recommend that because of potential security risk. You can transfer all your codes to the new phone in one go. See second link and video.

https://www.theverge.com/2023/4/24/23696058/google-authenticator-app-account-syncing-multiple-devices

https://www.techradar.com/how-to/how-to-transfer-google-authenticator-to-a-new-phone

Thanks so much!

You're Welcome