[Autofill] Decouple MaybeStartVoteUploadProcess() call from BAM

Before this CL, vote uploading in BAM::OnFormSubmittedImpl()
only happened if the BAM was still alive after Autofill AI's
asynchronous response.

This CL fixes that by
(1) inlining BAM::OnFormSubmittedAfterImport()
    at its only callsite, import_vote_and_log_metrics() in
    BAM::OnFormSubmittedImpl()
(2) conditioning the VotesUploader::MaybeStartVoteUploadProcess()
    call on the existence of the *client* instead of the *manager*
    (recall that the client owns the VotesUploader and indirectly
    also the manager, so
    - manager existence implies client existence but not vice versa;
    - client existence is sufficient for voting.)

Bug: 374086145
Change-Id: I6c2f81d39a40a7785354f1c9816bf45a27ca7833
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6142894
Reviewed-by: Dominic Battré <battre@chromium.org>
Code-Coverage: findit-for-me@appspot.gserviceaccount.com <findit-for-me@appspot.gserviceaccount.com>
Commit-Queue: Christoph Schwering <schwering@google.com>
Cr-Commit-Position: refs/heads/main@{#1402120}