Tracking the context is not enough, as we might clear the context to
avoid repeatedly reentering the same context.

Also fix unittests that relied on the default microtask queue getting
automatically processed instead of the one of the current context.

Bug: chromium:728583
Change-Id: Ia9a51c513fc7363a518af86cc54c5bda26b5fbe8
Reviewed-on: https://chromium-review.googlesource.com/c/v8/v8/+/2859850Reviewed-by: Toon Verwaest <verwaest@chromium.org>
Commit-Queue: Jochen Eisinger <jochen@chromium.org>
Cr-Commit-Position: refs/heads/master@{#74303}