[Desktop Android] Update TabsDuplicateFunction::Run() for porting

Update TabsDuplicateFunction::Run() to move away from non-cross-platform
concepts to only use types available on the experimental desktop android
platform. This will make it easier to port as cut-and-paste.

This CL should have no behavior change.

Bug: 371432155
Change-Id: I81a1d7f523222cfb8811ca3ea66dec2c7b14e9ca
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6838187
Reviewed-by: James Cook <jamescook@chromium.org>
Commit-Queue: Devlin Cronin <rdevlin.cronin@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1500516}