This might seem intuitive but it's wrong unless your phone is really old and unpatched. Modern phones sandbox everything, often encrypted per-application (standard on iOS for many years, becoming common on Android), and they have storage classes which will not be included in backups or easily copied to a computer.

You could start to approach that on a laptop — make sure you have FDE enabled, use the operating system's sandboxing features pervasively, store secrets using the TPM, etc. but that's a huge amount of work and the attack surface for apps on your laptop is enormous, especially for developers: how many people using a system like the one described are one unlucky npm install away from sending their TOTP seed to an attacker? The equivalent attack requires a system compromise on a phone (which tend to have 7+ figure USD bounties on iOS).