[Fix It] Calculate host status when EligibleHostDevicesProvider notifies

Exposes EligibleHostDevicesProvider::Observer interface that notifies
HostStatusProviderImpl of when it has finished processing newly
synced devices via OnNewEligibleDevicesSynced(). The
HostStatusProviderImpl calculates the host status in
EligibleHostDevicesProvider::OnNewEligibleDevicesSynced() rather than
DeviceSyncClient::OnNewDevicesSynced() to prevent host status being
calculated from an outdated eligible device cache that hasn't been
finished being updated by the EligibleHostDevicesProvider.

via logs that the host status was calculated after the
EligibleHostDevicesProvider processed the newly synced devices
and notified HostStatusProviderImpl.

Tested: Manually went through Multidevice setup flow and observed
Bug: b/320789583
Change-Id: Ifc2e0a14235b823a6732708fa85fe593c6c2ab42
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5405425


Reviewed-by: Jon Mann <jonmann@chromium.org>
Commit-Queue: Juliet Lévesque <julietlevesque@google.com>
Cr-Commit-Position: refs/heads/main@{#1280430}