I always save the key & qr code when setting up 2fa, in a seperate not-frequently-accessed keepass db. that way, when/if I change phone, I can re-set up the 2fa same as before,vfrom same qr codes and/or keys.
I’m a bit different in that I only save the backup code to the separate KeePass DB. I hadn’t even considered saving the key/QR code to it, which seems just as secure as what I do now.
Is it not that by each backup code, you can enter into account only once, whereas by key and/or qr code, you can essentially setup a new device to provide TOTP?
Well the backup code is for emergency situations (ie. to set up your replacement device and get a new backup code)! Sometimes they give you more than 1, E.g. Google gives 10. I have had the worry though, imagine using it and your PC crashing immediately..