- Add a new `tsc:check` script to ensure that there are no TS files with
  undetected errors.
- Split the TS configs in `integrations` so the compiled proto TS files can
  underly much stricter configuration requirements than the test files
  themselves.
- Add `DOM` to `compilerOptions.lib` for integration tests to have DOM's
  `AbortSignal` in scope.
- Apply the strictest TS preset there is to the compiled proto TS files (with
  a few exceptions that may be resolved later).
- Update the generated code to adhere to the stricter TS config.
- Modernise a few areas of the generated code.
- Add `tsc:check` to the CI script