Update ContactEditor to use a Profile-aware PersonalDataManager.

Bug: 40689806
Change-Id: If7f92f066a10ab45cd1daf8e4a88c69d547b2fe4
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5372759


Commit-Queue: Ted Choc <tedchoc@chromium.org>
Reviewed-by: Rouslan Solomakhin <rouslan@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1273115}