[ios][feed] Re-add bg timestamp and other timestamps.

The separate timestamp for background refresh was useful, and now
we want to make it available again.

This is not a full revert of the CL below. It does not revert the
default false for following feed background refresh.

Original change's description:
> [ios][feed] Remove bg timestamp & default false following feed bg refresh
>
> Change-Id: If5a2f09c5bf7aed2e140bad0c712c8ae6e899dbb
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3835267


> Commit-Queue: edchin <edchin@google.com>
> Reviewed-by: Sergio Collazos <sczs@chromium.org>
> Commit-Queue: Sergio Collazos <sczs@chromium.org>
> Auto-Submit: edchin <edchin@google.com>
> Cr-Commit-Position: refs/heads/main@{#1036201}

Change-Id: I404e9fa4d34b68173441b1b475112a012d349571
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3887205


Reviewed-by: Sergio Collazos <sczs@chromium.org>
Commit-Queue: edchin <edchin@google.com>
Cr-Commit-Position: refs/heads/main@{#1045542}