[Autofill] Introduce AutofillPredictionImprovements::GetAutofillClient()

The access to an AutofillClient will be used for two unrelated purposes:
1. To move the import call out of BAM into APIManager.
2. To access AutofillClient's LogManager to log to
   chrome://autofill-internals.

Bug: 375603948
Change-Id: I5fd26fa3b55a8d7636c8f7216e2d3f5dd0b35a6a
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5965876
Commit-Queue: Christoph Schwering <schwering@google.com>
Reviewed-by: Dominic Battré <battre@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1375119}