chore: Removed unused deps from agent audit

[Abhijeet Prasad (AbhiPrasad)]

AI Summary

• Remove unused development and runtime dependencies across the monorepo.
• Relocate ESLint to the package that uses it.
• Remove stale root overrides and Changesets tooling.
• Remove unused Vitest configuration from the browser integration.
• Remove redundant type packages now provided by their underlying dependencies.
• Fix the Temporal AI SDK example’s NodeNext import extension.

Validation

• Ran relevant type checks, builds, and unit tests for each affected package.
• Verified OTEL tests against both v1 and v2 dependency sets.
• Ran the Braintrust API compatibility test.
• Verified package files and lockfile formatting.

Changeset

No changeset required because these are internal dependency and tooling cleanups with no user-facing behavior or API changes.