fix(clerk-js): Remove the hydrate cache change for session (#7329)

[octoper]

Description

Port of #7329

Checklist

• pnpm test runs as expected.
• pnpm build runs as expected.
• (If applicable) JSDoc comments have been added or updated for any package exports
• (If applicable) Documentation has been updated

Type of change

• 🐛 Bug fix
• 🌟 New feature
• 🔨 Breaking change
• 📖 Refactoring / dependency upgrade / documentation
• other:

[changeset-bot]

⚠️ No Changeset found

Latest commit: 6a44e2f

Merging this PR will not cause a version bump for any packages. If these changes should not result in a new version, you're good to go. If these changes should result in a version bump, you need to add a changeset.

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Project	Deployment	Preview	Comments	Updated (UTC)
clerk-js-sandbox	Ready	Preview	Comment	Dec 2, 2025 3:58pm

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✨ Finishing touches

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Post copyable unit tests in a comment
• Commit unit tests in branch vaggelis/port-7329-to-vincent-and-the-doctor

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