Similar to Issue 785621, we should make it possible to write general (browser-neutral) tests for Web Share Target. This is difficult because Web Share Target is not an API, it's something that gets invoked from a user-agent-specific source (an operating system intent, or similar). It also requires that the receiving application be registered in a user-agent specific manner.
We would need a WebDriver API that lets a test harness automatically nominate a particular application (manifest) to receive a share, and fires a share payload at it.