Each implementation calls the exact resolution helpers its provider's
discovery uses (same env fallbacks, same OS branches, same closure
overrides), so doctor reports precisely where discovery looks and a
stale override or moved data dir stops being a silent $0.00.
lingtai-tui deliberately reports its candidates pre-existence-filter:
getLingTaiHomes drops non-existent dirs (right for discovery, wrong for
doctor, whose job is to show where it looked).
tests/provider-probe-roots.test.ts locks the mirroring: where a factory
takes an override, the same override must come back through probeRoots.
