Finally I have managed to make ESP32 development board to work as FIDO2 Authenticator device. I have trimmed a lot of functionality to achieve this. For example, I have implemented only one credential which is stored in volatile memory. User validation and presence is implemented as click with single button.
Nevertheless, I was able to pass both "Make Credential" and "Get Assertion" procedures on https://webauthn.bin.coffee/ webpage.
So, so far I have almost all required pieces to continue with the build of personal Authenticator device.