When asked to set up TOTP, the first thing I do is scan the QR code with a QR code reader, and save the secret into my password manager, before adding it to my authenticator app.
However, this does reduce the separation of factors, if that password manager is the same one containing your actual password.
Depending on your threat model this may be an issue.
1password lets you see it after you've saved it too.
As does Bitwarden (just "edit" and it is revealed)
Does this actually work? I thought most TOTP codes were single use. Have you actually tried re-using them?
The initial QR code isn't a TOTP code, it contains the secret used to generate the TOTP codes.
The QR code contains the TOTP key, which is the seed that's used to generate the codes, which form a time-based pseudorandom sequence.
You can absolutely scan the QR code with multiple authenticator apps (or copy paste the seed value into them) and they will all produce the same codes in the same order going forward.
Oh, that's actually really nice, I should start doing the same thing myself