Move storage/ to use new base::Pickle functionality

This moves to using the new base::Pickle creation factories,
opting for a safer internalized memory.

Bug: 330028190
Change-Id: I512ee7441c1914a8b032acfbd5e819667c5cffed
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5378392


Auto-Submit: Avi Drissman <avi@chromium.org>
Reviewed-by: Ayu Ishii <ayui@chromium.org>
Commit-Queue: Ayu Ishii <ayui@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1277003}