The main body of Web Share tests are found in external/wpt/web-share (imported from Web Platform Tests). However, many of those tests are necessarily manual (since they involve user interaction).
The tests in this directory are Chromium-specific automated versions of the manual tests from WPT. They use user-gesture hacks and a mock Mojo implementation to fully automate the API tests. These should be kept in sync with the upstream manual versions of the tests.