Slim the base projects command engine

[codeforester]

Context

cli/python/base_projects/engine.py remains an 808-line command engine. It mixes command dispatch, argument validation, workspace clone, status/check/doctor dispatch, and project command resolution.

Scope

• Extract project command dispatch and/or workspace clone orchestration into focused modules.
• Keep the public base_projects.engine entrypoint and command behavior stable.
• Preserve compatibility imports only where tests or callers require them.

Validation

• base_projects focused tests for command dispatch, workspace clone, and project resolution.
• A wrapped command smoke check for basectl projects/basectl workspace behavior if practical.
• git diff --check.