Travel to UK with child with both British/Japanese passports new UK ETA requirements

Hi, this will be the first time going back to the UK since the ETA was introduced (and since they got their UK passport).

My child has dual citizenship and both UK and Japanese passports.

I assume that they leave/enter Japan using their Japanese passport, and then enter/leave the UK using their British passport. Filling out the passport information on the airline website, should I put their Japanese or UK passport details? If I put the Japanese one I wonder if they airline will ask about their ETA. If I put the British one then it might seem like they are leaving and entering Japan as a non-national.

Has anyone done this trip since the new ETA was introduced, which passport information did you submit etc.?

Thanks for any feedback.