Move from ParseAndClassifyIdentifier to places where we either know that what
we're parsing are parameters, or where they could become (async) arrow formals.

Change-Id: Ic69bb586ed29ba9ac7b4dbef5d11a2e1954e7332
Reviewed-on: https://chromium-review.googlesource.com/c/1356503Reviewed-by: Camillo Bruni <cbruni@chromium.org>
Commit-Queue: Toon Verwaest <verwaest@chromium.org>
Cr-Commit-Position: refs/heads/master@{#57957}