SimpleX Chat - a private and encrypted messenger without any user IDs (not even random ones)! Make a private connection via link / QR code to send messages and make calls.
Having unique one-time (non-reusable) invite ID is great.
The wat SimpleX uses one-way queues, and then distributes those queues among servers offers a way to mitigate communication correlation (if the servers are independent and won't collude). Or you can just self host and not worry. Self hosting an onion service is easy.
Running SimpleX through a tor proxy (or VPN) offers even more advantages (if you think you need them).
Perhaps the only downside is SimpleX still controls who gets to be a public server (anyone can self host or offer servers, but they won't be integrated). I have no way of knowing if the servers are owned by a single entity. This part is not "open".