Google has coded their App Engine to read a 'push manifest' generated by a tool they publish [2]. Akamai gives you a GUI [3]. Cloudflare wants you to manually set headers [4] defined by the brand-new W3C draft 'preload' [5]. Last year, the Caddy devs blogged that HTTP/2 Push is essentially a big exercise for the reader/implementer [6].
I'm currently unaware of any web application framework which exposes idiomatic hooks to use HTTP/2 to push additional resources to the server. There are some generic server push addons or plugins that use older techniques from the websocket or pre-websocket days.
[1] https://news.ycombinator.com/item?id=12224258
[2] https://github.com/GoogleChrome/http2-push-manifest
[3] https://blogs.akamai.com/2016/04/are-you-ready-for-http2-ser...
[4] https://blog.cloudflare.com/announcing-support-for-http-2-se...
[5] https://www.w3.org/TR/preload/#server-push-http-2
[6] https://caddyserver.com/blog/implementing-http2-isnt-trivial
Even server push can be abstracted away via a cache. Pushed resources fill the cache, and when the application tries to fetch those resources the underlying HTTP/2 library could return the cached resource. This should be quite interesting to API clients, so that services don't have to make aggregate resource endpoints just to avoid round trips.
I do think future applications will want to have code triggered when a pushed resource arrives, though. I'm not aware of anyone doing this but it could be an interesting alternative to long-polling or streaming. That said, long-polling and streaming become very attractive within HTTP/2 as well, so it'll be interesting to see what developers end up doing.
However this is not something that is limited to HTTP/2. In principal you could do the same with HTTP/1 as the request and response bodies were also already streams. However there are some limitations to that: At first most HTTP/1 implementations do only allow a certain amount of parallel HTTP connections, which means long-running streams are not useful because they block off other requests. The second issue is that many HTTP library implementations (including XHR browser API and the current fetch API) do not allow to read the bodys in streaming form. This is also the blocker for having full grpc support in the browser. WIP browser APIs (fetch API with readable stream support) will allow to make use of these capabilities, for HTTP/2 and HTTP/1.