Docs & tests: dist/tool/extension management

**Summary**
Document the new CLI surfaces and add tests (unit/BDD/integration happy-path) covering global-first and local override.

**Scope**
- CLI docs: dist/tool/extension commands, flags, examples; troubleshooting (unsupported platform, missing selection, local vs global).
- Tests: handler/unit + BDD/integration happy-path for dist/tool/extension (global and local cases).
- Note manifests are JSONC (comments allowed, `.json` extension).

**Acceptance**
- Docs pages added/updated.
- Tests in place and passing for at least the happy paths.
- Troubleshooting section includes local/global guidance and common errors.

Start with the dist/tool/extension CLI surfaces and inspect the existing handler/unit and BDD/integration test structure. Cover global-first and local-override happy paths, then add documentation for commands, flags, examples, JSONC manifests, platform and selection errors, and local/global guidance. Done means the documentation is updated and the happy-path tests pass.

Written by the indexing model from the issue text.