well, disappoint.. show a shiny tool, then say how it took 6+ years to develop, and wont likely be open sourced. yes.. lot of us would like to implement something similar, just dont have the engineering resources to flush it out.
if I had to take a stab at it, I'd say a good place to start is some ELK platform. Seems like it has almost all of the right components to build something like this. Just curious if they have their apps directly feeding exceptions, or if they are slurping logs.
It's very hard to do this kind of thing by slurping logs (and is generally why ELK isn't considered a replacement for these tools). The first thing applications like Haystack try to solve is context. While I can't speak for Haystack (as I've never used it), Sentry using it's SDKs pulls in a ton of information that you would never get, or would at least be very hard to pull from logs. Examples of this include most of the HTTP request information, the authenticated user, context locals and surrounding code in the stacktrace, as well as any arbitrary context you might want to associate with it.
if I had to take a stab at it, I'd say a good place to start is some ELK platform. Seems like it has almost all of the right components to build something like this. Just curious if they have their apps directly feeding exceptions, or if they are slurping logs.