>BYOK E2EE messaging based on the same nomadic keys
Yes, this is already possible. A message can be encrypted with recipient's public key and included in a signed activity. Then recipient decrypts the message with their secret key. Keys are stored on the client side, so server operators can't see the plain text messages.
However, I am not familiar with modern encryption schemes like Olm and MLS. They might require additional keys.
>“Nomadic metadata,” e.g. metadata that follows your nomadic identity across multiple instances, such as global reputation or karma
The user is in control of their data, they decide which objects to keep and which to discard. I think nomadic karma system would not be reliable, because people will remove anything negative from their profiles, but a system of achievements might work.