[2025-04 back-fix] 🍪 Hydrogen Cookie Migration for New Shopify Cookie Architecture

[kdaviduik]

WHY are these changes introduced? + WHAT is this pull request doing?

Applies the same changes as https://github.com/Shopify/hydrogen/pull/3309, but back-fixed to the 2025-04 branch.

• Notably, 2025-04 is using Remix, whereas that PR ^ is using React Router 7

We are doing this because the old cookies will stop working on May 1, 2026. This will break Shopify analytics for any merchants who haven't yet upgraded to a new Hydrogen version that works with the new cookies (while also being backwards compatible with the old cookies). Because May 1st is <365 days away, we are back-fixing past versions of Hydrogen so that all merchants using a Hydrogen version released in the last year will only have to do a minor version bump!

HOW to test your changes?

Run the e2e tests locally!

Post-merge steps

1. Once this has merged into 2025-04, we should get a PR automatically opened up on this branch by the back-fix workflow
2. Before merging that PR, we need to fix the issue with our npm release tokens
3. Once that's fixed, we can merge that PR into this branch and it should do the npm release!
4. Update docs/changelog.json with upgrade instructions!

Checklist

• [x] I've read the Contributing Guidelines
• [x] I've considered possible cross-platform impacts (Mac, Linux, Windows)
• [x] I've added a changeset if this PR contains user-facing or noteworthy changes
• [x] I've added tests to cover my changes
• [x] I've added or updated the documentation