[Extensions] Fix inspecting background worker for split mode extensions

This CL adds to the logic for opening devtools for an extension service
worker associated with an incognito profile for a split more extension.

Also adds a new test case to the associated apitest to cover this case
and does a little refactoring in that test file.

Bug: 1350669
Change-Id: I3df96f0f34c8b6e46851711926d9a029291003d2
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4044884
Reviewed-by: Devlin Cronin <rdevlin.cronin@chromium.org>
Commit-Queue: Tim <tjudkins@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1075396}