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This prepares future changes to read the user DM token by moving the
DM token reading code to ConnectorsService.

This also moves and adds the incognito mode check to ConnectorsService
instead of having it in random code locations.

Bug: 1148789, 1149425
Change-Id: I70779d2af97735ed76271a2d0cadf7b9956411f4
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2537933Reviewed-by: Daniel Rubery <drubery@chromium.org>
Commit-Queue: Dominique Fauteux-Chapleau <domfc@chromium.org>
Cr-Commit-Position: refs/heads/master@{#836121}