Sage is Salvia officinalis, and its name is the whole argument for its reputation. The Latin salvia derives from salvere, to be well or to be saved; officinalis marks it as a plant of the apothecary's store room. The name is a claim about the plant, embedded in the botany.
The proverb usually quoted, why should a man die who has sage in his garden?, is genuinely old, appearing in the medieval Latin of the Salerno school as cur moriatur homo cui salvia crescit in horto, and the school's verse health regimen was one of the most widely copied medical texts in medieval Europe. The proverb is real; the claim in it is not.
Culpeper assigns sage to Jupiter, and the reasoning is legible: Jupiter in his scheme is the expansive, preserving, benefic planet, and a herb whose reputation is longevity and general well-being falls there almost by definition. Sagittarius follows by rulership, as a later derivation rather than as Culpeper's own step.
The pharmacology is modest but not nothing. Sage contains thujone, as its Artemisia relatives do, along with camphor, cineole and rosmarinic acid, and it has demonstrable antimicrobial and astringent properties consistent with the traditional gargle for sore throat. There has been some investigation of Salvia officinalis and Salvia lavandulaefolia extracts and cognitive measures, with small and not firmly established results. High-dose or prolonged use of thujone-rich preparations is not benign.
Sage darkens and coarsens with age in the garden and is generally replaced every few years, which is a small irony for a longevity herb.