You would need to use a messaging app that routes your traffic over Tor, or some other anonymizing network. Some options like Ricochet or Tor Messenger are being developed.

Would love to know.

Wire reduces metadata, e.g. no phone number and no social network/contact graph for triangulation. You can use a throwaway email to register, that is never used in other contexts. That leaves metadata for device key fingerprints, Wire account ID and public IP addresses.

Wire also uses WebRTC for some communication, not sure about the metadata implications of that protocol.

I2P Messenger, I2P's Bote mail