Migrate to TSDown

[frandiox]

Since Vite 8 uses Rolldown I thought we could migrate the build tool also to it. TSDown is the successor of TSUp 🙃

Build time improves by ~33%

[github-actions]

We detected some changes in packages/*/package.json or packages/*/src, and there are no updates in the .changeset.
If the changes are user-facing and should cause a version bump, run pnpm run changeset add to track your changes and include them in the next release CHANGELOG.
If you are making simple updates to examples or documentation, you do not need to add a changeset.

[shopify]

Oxygen deployed a preview of your fd-tsdown branch. Details:

Storefront	Status	Preview link	Deployment details	Last update (UTC)
Skeleton (skeleton.hydrogen.shop)	✅ Successful (Logs)	Preview deployment	Inspect deployment	March 25, 2026 6:37 PM

Learn more about Hydrogen's GitHub integration.