Cherry pick PR #9816: Cherry pick Storage Migration Rework to 26.eap

[cobalt-github-releaser-bot]

Refer to the original PR: #9816

Cherry pick Storage Migration Rework from 26.android to 26.eap, fixed incompatibilities in 26.eap branch, hooked up storage migration trigger in CobaltBrowserMainParts::InitializeMessageLoopContext() and added migration status telemetry, verified the whole workflow on linux-x86x11.

Test: Locally verified storage migration manager on linux-x86x11:
Full Log: https://paste.googleplex.com/5720103317536768#l=1
https://screenshot.googleplex.com/8k4Sc7pTzxreach
Bug: 489453068

[cobalt-github-releaser-bot]

Caution

There were merge conflicts while cherry picking! Check out cherry-pick-main-9816 and fix the conflicts before proceeding. Check the log at https://github.com/youtube/cobalt/actions/runs/30123635189 for details.

[github-actions]

🤖 Gemini Suggested Commit Message

---

cobalt: Rework storage migration logic

Integrate the reworked storage migration pipeline into the 26.eap
branch. This migration transitions legacy Starboard cookies and local
storage data into the Chromium-based storage system during initial
browser startup.

The logic is hooked into the browser initialization flow to ensure data
consistency before the web application loads. It includes telemetry for
tracking migration outcomes and durations, a sentinel file to prevent
redundant operations, and a command-line switch to disable the
migration process.

Bug: 489453068

---

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