Centralize canonical system/user and deterministic renamed-bundle path facts. Reuse the installer destination and honor the same local candidates in doctor and runtime; scan renamed bundles only after canonical candidates fail. Preserve explicit path spelling and exclusive selection. Homebrew command probing remains doctor-only with explicit runtime configuration guidance.
Validation: owner, config, setup and doctor tests cover canonical priority and renamed paths; public CLI verifies explicit path preservation without launching Hopper. No real Hopper analysis claimed.
Fixes#3054
Related: #3085
Co-authored-by: Vinícius DS Andrade <95101505+viniciusdsandrade@users.noreply.github.com>
Co-authored-by: Kaoru0822 <208281322+kaoru0822-kitauji@users.noreply.github.com>