Reland "SET: Propagate the callback error to the caller / devtools."

This reverts commit ccdbd4ce097bf56a2ae5a65f9d77c56f2a61ee7c.

Original change's description:
> SET: Propagate the callback error to the caller / devtools.
>
> This patch propagates the error up from the callback. Without this
> patch we just know that an exception happened in a promise, but with
> this we actually know what the error is, which makes it easier to
> debug callbacks.
>
> R=khushalsagar@chromium.org
>
> Change-Id: I85a70f613e01fb1206365e7460edb805edd5fe53
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3807891
> Reviewed-by: Khushal Sagar <khushalsagar@chromium.org>
> Commit-Queue: Vladimir Levin <vmpstr@chromium.org>
> Cr-Commit-Position: refs/heads/main@{#1032649}

Change-Id: I4dff4e5f8d2afce3f9537a2fb1d780f64bd976fc
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3820601
Reviewed-by: Khushal Sagar <khushalsagar@chromium.org>
Commit-Queue: Khushal Sagar <khushalsagar@chromium.org>
Commit-Queue: Vladimir Levin <vmpstr@chromium.org>
Auto-Submit: Vladimir Levin <vmpstr@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1033736}