Repairs TypeScript check-types across the monorepo and adds a CI gate so
regressions are caught going forward:
- core: bundler module resolution and strict-mode fixes
- sdk-js: bundler module resolution; keep codegen, formatter, packaging working
- react-core: fixes across components, hooks, and tests
- react-native: restore catch binding referenced by TypeError cause
- runtime: repair check-types and bound AI SDK schema inference
- web-inspector: nodenext import extensions, export Anchor
- remaining packages and node example: assorted check-types repairs
- deps: add missing type-only devDependencies
- license context driven from /info licenseStatus
- ci: run check-types in the static quality workflow
Squashed from 12 commits for a single, easily-revertable change.