[Signin][Android] Update createWithoutBadge be created after native

In previous Cls profileDataCache was updated to require native by adding
an identityManager object in the constructor. This CL updates
profileDataCache#createWithoutBadge to use this constructor.

IdentityDiscController will now show the button only if the profile has
been initialized.

Bug: 342205162
Change-Id: Iba6741426576ee3dde9e8d3dc76901c1294a49d8
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6772490
Reviewed-by: Menghan Yang <myuu@google.com>
Reviewed-by: Patrick Noland <pnoland@chromium.org>
Commit-Queue: Liza Bipin <mlbipin@google.com>
Cr-Commit-Position: refs/heads/main@{#1495306}