Where is the guarantee that the manufacturer doesn’t know the key?

Initially, the card comes without a private key. The key is generated when the wallet is created, and the card is scanned to the device.

Moreover, if you reset the card to factory settings and create a new wallet, new public and private keys will be generated.

The Tangem firmware has undergone two independent audits: the first in 2018 by Swiss company Kudelski Security and the second in 2023 by international security lab Riscure.
Both audits confirmed the system's integrity, finding that the private key is generated using a random hardware number generator and that no backdoors or bugs can lead to loss of funds.

You can read the detailed reports of both audits. Kudelski Security's audit results are available here, and information about the second audit conducted by Riscure can be found here.