Buying new phone.2FA question

My phone was Android and died a few days ago.I am planning to switch to IOS and my question is will have any problems with the 2FA authenticator. So far i have been using Google 2FA and if i plan to switch it will the security codes you receive once you set up 2FA authentication on Binance,Kucoin be enough or i will need a code from Google too ?

I am asking because everywhere i read people say you need a QR code from Google to restore access to your 2FA account and obviously i cant do that because my phone is broken.

I keep all the 2FA codes from the different sites written on paper so that's not worrying me.

Another question:Everywhere i see people saying that Google 2Fa is a bad authenticator app.What 2FA apps would you guys recommend ?

Thanks in advance !