That is better than nothing.
That is true – indeed, I can’t understand why that warning is missing. There even is a feature request about that: Recommend vault export before changing master password
As a general rule: make an export of your vault before making any critical change (like changing your BW email address, master password, KDF, setting up 2FA, …), just in case.
On the other hand: all 2FA settings should be unaffected by changing the master password – and that alone can’t explain why you lost your “authenticator app” 2FA. – As implied before, my guess would be that you only synced your TOTP codes from your vault with the authenticator app. And when you changed your master password, you also “cut off” the sync between the password manager and authenticator app. (as the password manager app got logged out due to the master password change)
If you had stored your TOTP code locally on the authenticator app, a master password change shouldn’t affect that in any way.
Anyway, can’t be changed now – but for the future: don’t store your “authenticator app” 2FA in only one location. (hence the emergency sheet… where you can also store the “authenticator key” / TOTP seed code for “authenticator app” 2FA)