using a ZKP for client-server compatibility check might provide useful privacy advantages.

I'm not sure what this issue is proposing a change for. There is no specific compatibility check in Fabric API, and the closest functionality is registry sync, which is required for general protocol compatibility.

there's no compatibility check in ping packet?

There never was in fabric. There are 3rd party mods for that through

Its an intresting idea maybe something to consider if/when we add this, but yeah we currently do not send the mod list.

Its not something I knew existed before I quickly looked up what it was. Adding something like this may involve some complex code that may open us up to possible security vulnerabilities.