(1) the tillitis CA certifies your TKey device platform. You can now trust that it's running a specific firmware version with some platform pubkey.
(2) Your custom software is running and derives a keypair from it's derived secret + program binary hash.
(3) Somehow your custom software's pubkey gets locally certified by the platform's pubkey from (1). (not sure what this looks like w/ the TKey)
You now have a chain of trust from (1) the tillitis CA -> (3) the TKey device platform pubkey @ some specific firmware version -> (2) your custom software pubkey @ some specific version.
Now that we have a trusted pubkey for our service, I would open a secure channel to it via Noise IK or something (https://noiseexplorer.com/patterns/IK/). The TKey platform definitely looks a bit anemic so getting this working might be a challenge...