Does Sentry provide a way to access raw issue data so that I can build my own analytics on that?

You can access the raw event data through Sentry's API, and more specifically, the List a Project's Error Events endpoint. Make sure to set the full query parameter to true to include the full event body, including the stacktrace, in the event payload.

If you need to see all the events from a specific issue, you can use the List an Issue's Events endpoint instead, which works in a similar way as the above.

Another option is to export the data in CSV format. For more information, please check this article.