Wavy dot is meant as a syntax tool to help with eventual-send. The major difference between what is suggested here and eventual-send is pipelining. In a single agent there is no difference, but in distributed systems (e.g. between Workers, or between a client and server), you want to avoid paying the round trip costs, which here would occur because of the intermediary awaits.
To take the above example, you want to send as soon as possible fetchBaz() to the result of fetchBar() which was itself send to the result of fetchFoo(). You only want to await the result of fetchBaz(). Results are represented by promises, and sending a message to a promise means sending the message to the system that is currently in charge of deciding that promise.
These proposals are a little stale, but Agoric has been using these mechanisms for years. eventual-send has a shim in the endo repository, which uses a E helper in place of the ~. syntax. The developer documentations are lacking / out of date, and I believe there is a strong dependency of the eventual-send package on SES for now. There is a Matrix room where you may be able to get some questions answered.
Btw, the pipeline operator will probably be a good approximation of the benefits of wavy-dot, at least until that kind of distributed patterns emerges more fully.
With await:
const baz = await fetchFoo() |> await %.fetchBar() |> await %.fetchBaz();
With E:
const baz = await (fetchFoo() |> E(%).fetchBar() |> E(%).fetchBaz());
With wavy-dot:
const baz = await fetchFoo()~.fetchBar()~.fetchBaz();