Can set cookie for root domain, but not for higher level domain

Question

I am hosting my BE from beta.zaharzagrava.ngrok.io and my FE from teta.zaharzagrava.ngrok.io. Setting cookie for zaharzagrava.ngrok.io works just fine:

1. I send a request to beta.zaharzagrava.ngrok.io with withCredentials=true.
2. beta.zaharzagrava.ngrok.io sets http-only secure cookie on zaharzagrava.ngrok.io

But if I try to do the same to set cookie for ngrok.io domain id does not work.

I understand that ngrok.io is a 3rd party services, but technically shouldn't I be able to set cookie for ngrok.io in exactly the same way I did for zaharzagrava.ngrok.io?