Revert "[Profile creation] Split Dice-specific signin logic from the generic one"

This reverts commit b9f7f787.

Reason for revert: Broke accessibility tests
https://ci.chromium.org/ui/p/chromium/builders/ci/Mac10.11%20Tests/65137/overview

Original change's description:
> [Profile creation] Split Dice-specific signin logic from the generic one
>
> This CL splits the Dice-specific sign-in logic (now called
> ProfilePickerDiceSignInProvider) from the Dice-agnostic signed-in
> profile creation logic (now called ProfilePickerSignedInFlowController).
> This unblocks reusing the generic part of the code for lacros. It is
> (almost) pure refactoring, with no noticeable behavioral changes (that
> only requires minor changes in tests).
>
> To simplify reviewing, both new classes are kept in the same .h and .cc
> files. They will be split into separate units in a trivial follow-up.
>
> Bug: 1227029
> Change-Id: Ic6e0df8f7c3543c69fbd872cc52e9f57c8a0c72a
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3107008


> Commit-Queue: Jan Krcal <jkrcal@chromium.org>
> Reviewed-by: Stefan Kuhne <skuhne@chromium.org>
> Reviewed-by: Kush Sinha <sinhak@chromium.org>
> Cr-Commit-Position: refs/heads/main@{#915904}

Bug: 1227029
Change-Id: I4a59216088b930e186b877a7750ed9a6f02bf69c
No-Presubmit: true
No-Tree-Checks: true
No-Try: true
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3124815
Auto-Submit: Vasilii Sukhanov <vasilii@chromium.org>
Commit-Queue: Rubber Stamper <rubber-stamper@appspot.gserviceaccount.com>
Bot-Commit: Rubber Stamper <rubber-stamper@appspot.gserviceaccount.com>
Cr-Commit-Position: refs/heads/main@{#915944}