Save tab after restoring the archived tab

When restoring the inactive tabs without opening them, the timestamp will be updated. But the tab isn't saved to disk with the timestamp change.
It caused the retored inactive tabs will be re-archived on the next cold
start unless it is opened by user. Save the tab to disk after restoring the archived tab.

Bug: 374903789
Change-Id: I91e2cf8f354b01d29fcefaaf89c0258294d29cac
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5952666
Reviewed-by: Brandon Wylie <wylieb@google.com>
Commit-Queue: Calder Kitagawa <ckitagawa@chromium.org>
Reviewed-by: Calder Kitagawa <ckitagawa@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1373903}