Summary

• Add non-dry-run installer coverage for fresh clone/setup, idempotent reruns, BASE_HOME default install directory, unwritable target failure, and installed runtime files.
• Use a fake supported Bash in tests so setup/update-profile calls are hermetic while the git clone path remains real.
• Honor BASE_HOME as an installer directory fallback when BASE_INSTALL_DIR is not set.

Validation

• bats tests/install.bats
• env HOME=/private/tmp/base-review-home BASE_TEST_PYTHON=/Users/rameshhp/.base.d/base/.venv/bin/python bin/base-test
• git diff --check

Closes #299