Incorrect, unless you choose not to record your seeds anywhere else, which is not a 2fa problem.
2fa is in the end nothing more than a 2nd password that just isn't sent over the wire when used.
You can store a totp seed exactly the same as a password, in any form you want, anywhere you want, and use on a brand new device at any time.
You know google authenticator app introduced a backup feature less than 1 year ago right?
You know phones break all the time right?
When I said they are just another password, I was neither lying nor in error. I presume you can think of all the infinite ways that you would keep copies of a password so that when your phone or laptop with keepassxc on it breaks, you still have other copies you can use. Well when I say just like a password, that's what I mean. It's just another secret you can keep anywhere, copy 50 times in different password managers or encrypted files, print on paper and stick in a safe, whatever.
Even if some particular auth app does not provide any sort of manual export function (I think google auth did have an export function even before the recent cloud backup, but let's assume it didn't), you can still just save the original number the first time you get it from a qr code or a link. You just had to know that that's what those qr codes are doing. They aren't single-use, they are nothing more than a random secret which you can keep andbcopy and re-use forever, exactly the same as a password. You can copy that number into any password manager or plain file or whatever you want just like a password, and then use it to set up the same totp on 20 different apps on 20 different devices, all working at the same time, all generating valid totp codes at the same time, destroy them all, buy a new phone, retrieve any one of your backup keepass files or printouts, and enter them into a fresh app on a fresh phone and get all your totp fully working again. You are no more locked out than by having to reinstall a password manager app and access some copy of your password db to regain the ordinary passwords.
The only difference from a password is, the secret is not sent over the wire when you use it, something derived from it is.
Google authenticators particular built in cloud copy, or lack of, doesn't matter at all, and frankly I would not actually use that particular feature or that particular app. There are lots of totp apps on all platforms and they all work the same way, you enter the secret give it a name like your bank or whatever, select which algorithm (it's always the default, you never have to select anything) and instantly the app starts generating valid totp codes for that account the same as your lost device.
Aside from saving the actual seed, let's say you don't have the original qr code any more (you didn't print it or screenshot it or right-click save image?) there is yet another emergency recovery which is the 10 or 12 recovery passwords that every site gives you when you first set up totp. You were told to keep those. They are special single-use passwords that get you in without totp, but each one can only be used once. So, you are a complete space case and somehow don't have any other copiesbof your seeds in any form, including not even simple printouts or screenshots of the original qr code, STILL no problem. You just burn one of your 12 single-use emergency codes, log in, disable and re-enable totp on that site, get a new qr code and a new set of emergency codes. Your old totp seed and old emergency codes no longer work so thow those out. This time, not only keep the emergency codes, also keep the qr code, or more practical, just keep the seed value in the qr code. It's right there in the url in the qr code. Sometimes they even display the seed value itself in plain text so that you can cut & paste it somewhere, like into a field in keepass etc.
In fact keepass apps on all platforms also will not only store the seed value but display the current totp for it just like a totp app does. But a totp app is a more convenient.
And for proper security, you technically shouldn't store both the password and the totp seed for an account in the same place, so that if someone gains access to one, they don't gain access to both. That's inconvenient but has to be said just for full correctness.
I think most sites do a completely terrible job of conveying just what totp is when you're setting it up. They tell you to scan a qr code but they kind of hide what that actually is. They DO all explain about the emergency codes but really those emergency codes are kind of stupid. If you can preserve a copy of the emergency codes, then you can just as easily preserve a copy of the seed value itself exactly the same way, and then, what's the point of a hanful of single-use emergency passwords when you can just have your normal fully functional totp seed?
Maybe one use for the emergency passwords is you could give them to different loved ones instead of your actual seed value?
Anyway if they just explained how totp basically works, and told you to keep your seed value instead of some weird emergency passwords, you wouldn't be screwed when a device breaks, and you would know it and not be worried about it.
Now, if, because of that crappy way sites obscure the process, you currently don't have your seeds in any re-usable form, and also don't have your emergency codes, well then you will be F'd when your phone breaks.
But that is fixable. Right now while it works you can log in to each totp-enabled account, and disable & reenable totp to generate new seeds, and take copies of them this time. Set them up on some other device just to see that they work. Then you will no longer have to worry about that.
But if you forgot to do it on day one, you can't do it on day two because there is no way of getting them out other than rooting the phone.
Giving how your premise was wrong, I won't bother to read that novel you wrote. I'll just assume it's all derived from the wrong premise.
