chore: Upgrade typescript to 5.9.3

[emrysal]

Summary by cubic

Upgrade TypeScript to 5.9.3 across the monorepo for consistent builds and newer compiler features. Also aligns where TypeScript lives (dev vs peer) and tidies related deps.

• Dependencies

  • Replace all TypeScript beta refs with 5.9.3 and remove root TypeScript.
  • Move TypeScript to peerDependencies where appropriate (e.g., trpc, ui, atoms: ^5.1.0; embed-react/snippet: ^5.9.3) and add devDependencies in platform and eslint packages.
  • Normalize React peer deps (add react-dom where missing; move react to peer in ui) and remove next-seo from ui.
  • Update yarn.lock accordingly.

• Migration

  • Ensure TypeScript >=5.1 is installed for packages declaring it as a peer (embed-react/snippet need ^5.9.3).
  • Ensure react and react-dom ^18 or ^19 are present where required.
  • Run a fresh install; no runtime code changes expected.

^{Written for commit a49585b. Summary will update automatically on new commits.}