Revery is fully native and doesn't use parts of web platform. It uses ReasonML, that is dialect of OCaml and has its own implementation of platform and renderer.
The server part of Convos is like an IRC bouncer, but instead of supporting the IRC protocol from the client side, it has a HTTP/WebSocket interface that talks to the Convos frontend.
So Convos keeps your connection, so even if you close the web browser, you will still receive messages and you can see the history once you open your browser again.
If you stop the Convos server, then you will also be disconnected from the IRC server.
Lambda is cheap, API Gateway is expensive.
Lambda with API Gateway should be used for low or unpredictable volumes.
You can replace API Gateway by an ALB, which will be much much cheaper in the article use case.
Lambda is also great when it's triggered by everything but API Gateway. Analysing a file uploaded on S3, reacting to an SNS message or consuming messages in SQS.
It's self-hosted.
The website seems down at the moment though.