The F-Droid back-end contain sig & signer properties for each APK.
I finally figured out that the signer value can be found as Signer #1 certificate SHA-256 digest from the output of the apksigner verify --print-certs <apk> command.
However, I still can’t find where to get sig from.
Yes, and I did manage to make the official client work in v2 with my server.
But I still would like to solve this, firstly because the official client has a setting for forcing v1 which must be there for a reason, secondly because it would be highly frustrating as a developer to discard this issue, especially considering that I managed to make Neo Store work with my server, while that app uses v1.