SANITY originally meant "health" from the 1400s

SANE originally meant "healthy"

HEALTHY came into use as SANITY shifted to mean "soundness of mind"

SANITARY & SANITIZE enter the language in the 1800s, after it was discovered that clean surgery led to fewer infections https://twitter.com/MerriamWebster/status/1252809567630528514

SANE referred to physical health at first (this corresponds to the modern French word 'sain'/'saine').

As late as 1828, Noah Webster gave as his first definition:

Sound; not disordered or shattered; healthy; as a sane body.

#etymology #languagechange

By the time SANITARY, SANITATION, & SANITIZE were introduced in the 1800s, enough time had passed that there was no direct connection with physical health (SANITARY was never a synonym of HEALTHY as SANE had been), because of the evolution of the related terms.