As far as web frameworks go, WebSockets over HTTP/2 are supported in for example ASP.NET by default (https://learn.microsoft.com/en-us/aspnet/core/fundamentals/w...). There is however still a surprising amount of languages/libraries/frameworks/servers where the support is missing (e.g. go https://github.com/golang/go/issues/49918).
On the client side, both Chrome (https://chromestatus.com/feature/6251293127475200) and Firefox will use it when available, but I have encountered some issues with cross-origin support (https://issues.chromium.org/issues/363015174)