Reland "Stop Trigger UI when triggering a direct action"

This is a reland of commit ef0e429f

Re-landing from the UI didn't work because of merge conflicts so I did it manually.

Original change's description:
> Stop Trigger UI when triggering a direct action
>
> This stops the trigger UI and trigger script coordinator when a direct
> action is requested and prevents reuse of the trigger UI bottom sheet
> content by the script UI triggered by the direct action.
>
> Bug: b:209399694
> Change-Id: I9d1046a8fe79c061a75fa496912ed3480bfc2211
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3420909


> Reviewed-by: Luca Hunkeler <hluca@google.com>
> Reviewed-by: Clemens Arbesser <arbesser@google.com>
> Commit-Queue: David Bengoa <dbengoa@google.com>
> Cr-Commit-Position: refs/heads/main@{#970713}

Bug: b:209399694
Change-Id: I5e41a7c6c67b48f93d3a8db287a7991985e55270
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3610008


Reviewed-by: Clemens Arbesser <arbesser@google.com>
Commit-Queue: David Bengoa <dbengoa@google.com>
Cr-Commit-Position: refs/heads/main@{#999808}