The API is already available in all the major browsers, so nothing really changes with this announcement. The API itself lets you generate and manipulate audio data in a way that was impossible with just the HTML Audio tag.
Most of the Web Audio stuff has already been present in all major browsers for a little while, this mostly standardises what's already there. The main thing that this brings in that up until now was just a feature of Chrome is the AudioWorklet, so real-time low-level audio processing in JS worklets will work cross-browser when its implemented in the other browsers. It's very difficult to implement low-level audio processing off of the main thread in non-Chromium browsers at the moment.
AudioWorklet (which allows you to work with audio sample-by-sample in a dedicated, high priority "thread") is available and works well in Firefox and the latest Safari. I haven't tried it in Edge, but I believe it's also working well.
This is true for many web features, including many basic PWA features like web push notifications, url capture, etc...
As a mobile first web developer, ios is the thing that's really holding us back.
The very frustrating thing about this is that the end user tends to blame the app, and there's not a good way to communicate to them "hey, we would totally do this, but mobile Safari has limited functionality and Apple won't allow other browsers to be installed"