[codex] Add hermetic Base integration tests

[codeforester]

Summary

• Add a hermetic BATS integration suite that copies Base into a temporary workspace and runs real basectl launchers against fake project repos.
• Cover workspace discovery, setup/check/doctor, structured project JSON, basectl test delegation, profile dry-run behavior, and a Homebrew-style Base home with explicit workspace override.
• Add an integration job to the GitHub Actions test workflow and include the suite in bin/base-test.
• Document Base test layers and when to add integration coverage.

Validation

• BASE_INTEGRATION_PYTHON="$HOME/.base.d/base/.venv/bin/python" bats tests/integration/base_workflows.bats
• ./bin/base-test
• git diff --check

Fixes #294