https://github.com/gobengo please use the Bugzilla bug for Web Share API to check for info about Firefox support in particular. In this case it looks like it was implemented in Firefox 71: https://bugzilla.mozilla.org/show_bug.cgi?id=1312422 (also linked from the standards-position dashboard entry via the wrench).
You can also check the corresponding MDN page (also linked from the dashboard entry) if you only wanted to check whether or not Firefox (or another browser) supports it: https://developer.mozilla.org/en-US/docs/Web/API/Navigator/share#browser_compatibility
For Web Share Target API, I checked https://mozilla.github.io/standards-positions/#web-share-target and it also has a wrench icon link to its corresponding Bugzilla bug: https://bugzilla.mozilla.org/show_bug.cgi?id=1476515