Cache IDE diagnostic probes per IDE

[codeforester]

Summary

• Add an in-memory IDE diagnostic snapshot so check/doctor probes each IDE once per diagnostic collection pass.
• Reuse cached CLI availability, extension listings, settings paths, and parsed settings while preserving one finding per declared extension or setting.
• Add focused tests for extension and settings probe reuse.

Validation

• PYTHONPATH=lib/python:cli/python /Users/rameshhp/.base.d/base/.venv/bin/python -m unittest cli/python/base_setup/tests/test_ide_extensions.py
• PYTHONPATH=lib/python:cli/python /Users/rameshhp/.base.d/base/.venv/bin/python -m unittest cli/python/base_setup/tests/test_ide_settings.py
• env -u BASE_HOME ./bin/base-test
• git diff --check
• PYTHONPATH=lib/python:cli/python git ls-files -z '*.py' | xargs -0 /Users/rameshhp/.base.d/base/.venv/bin/python -m pylint --rcfile=.pylintrc

Closes #509