Every account I have setup with TOTP I also make sure to print out the recovery codes and put them in a safe, and use them if my device is ever destroyed. When I switch phones (which for me happens maybe once every 2-3 years at most), I go through the shitty process of transferring the TOTP codes over to the new device, but it doesn't really take all that long (it took me an hour to do it for about a dozen accounts last time I did it), and I'd much rather not have any of it uploaded anywhere.
You can print out the QR code or save that somehow during setup and use that to setup TOTP codes on other devices (or the same TOTP on multiple devices), but I tend not to do that as recovery codes work just as well, and they notify you if they are used (unlike a TOTP setup QR code). I did have to store the QR code for one account that doesn't provide recovery codes, but it's overall not that much extra work.