[iOS] Ensure new windows open with the right profile

Before this CL, new windows (opened via 3dot -> New Window, or via
long-press -> Open in New Window) would use the "last used" profile,
which is not always the one that actually triggered the new window to
be opened.
This CL fixes this by attaching the originating profile name to the
new-window command, and using that in attachProfileToScene.

This only makes a difference if kSeparateProfilesForManagedAccounts is
enabled, since otherwise there's only one profile anyway. (And also
only on iPads, since iPhones don't support multi-window.)

Bug: 410400557
Change-Id: I3f7d87bbbf77a593f9e88b8a9a9eb96a33e092fc
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6480953
Reviewed-by: Mark Cogan <marq@chromium.org>
Commit-Queue: Marc Treib <treib@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1450567}