You’re fundamentally misunderstanding how TouchID or FaceID work.
The biometrics authenticate you with the Secure Enclave in your phone. The enrolled biometric data is stored within the Secure Enclave and practically unrecoverable. Authentication is done directly within the Secure Enclave. The connection between the sensor (fingerprint, camera) and Secure Enclave is direct and encrypted.
Conceptually, this is identical to using a passcode or password to unlock your device.
Once the Secure Enclave is unlocked, your phone can use it to sign requests, decrypt data (e.g., stored passwords), etc. The signed request or decrypted password is what’s transmitted to the app, website, or whatever else you’re authenticating against.
Your biometric data never leaves a secure encrypted channel between the sensor and Secure Enclave, and within the Secure Enclave’s own storage.
It’s some seriously cool hardware and the lengths it goes to to mitigate a lot of common and uncommon attacks is impressive. (It has a separate built in voltage and clock monitor with a wider operating envelope so if you try and voltage glitch it, it can lock and disable itself and require a reset. Bet Nintendo wishes they had thought of that.)
There are a _lot_ of details published about this.
Secure Enclave: https://support.apple.com/en-ca/guide/security/sec59b0b31ff/...
Overall platform security: https://support.apple.com/en-ca/guide/security/welcome/web