feat(product): transfer state when hydrating backend from server to client

[damienwebdev]

PR Checklist

• [x] Commit message follows our contributing guidelines
• [x] Tests added/updated (for bug fixes/features)
• [x] Documentation added/updated (for bug fixes/features)

PR Type

• [ ] Bug fix
• [x] Feature
• [ ] Style update
• [ ] Refactor
• [ ] Test
• [ ] Build
• [ ] CI
• [ ] Docs
• [ ] Performance
• [ ] Other (please describe)

Current behavior

Part of: #4143

New behavior

Product backend data is transferred when hydrating backend from server to client.

Breaking change?

• [ ] Yes
• [x] No

Additional context

Depends on #4147