#243)

The docs BugPlayground only ever showed one program; the example
picker lived in the standalone packages/playground app. Port a lean
version into the docs widget (gnidan #33).

- bugc-react: add a curated `bugExamples` set (Counter, Function calls,
  Arrays & loops) as a reusable export. Sources are distilled from
  packages/bugc/examples and stripped of the `/*@test*/` behavioral
  annotations the raw files carry, so they read cleanly in an editor.
  examples.test.ts asserts each compiles to bytecode without errors
  (guards against a typo in an inlined source); adds the missing
  vitest.config.ts so the package's test script runs.
- web BugPlayground: add an optional `examples` prop (defaults to
  bugExamples) and an Example dropdown in the header controls. The
  selector shows only when no `initialCode` is passed — so the bare
  playground page gains it while inline single-example doc embeds stay
  unchanged. Selecting an example loads its source and recompiles.

Additive; does not affect the tracer or #227. Example sources verified
to compile via the new tests; UI wiring mirrors the existing optimizer
selector.