A question about the word 'spirit' used to mean a phonetic 'breathing'

Although the subject is all Greek to me (literally and figuratively), it does appear that these breathing marks were referred to as "spirits" in a number of works, all of which are pretty old.

The spirits are two, a rough and a gentle; a rough, is a Semicircle tending towards the right hand thus ( ̔ ).
_{An English-Greek Lexicon, containing the derivations, and various significations of all the words in the New Testament, 1661}

The Grammarians call a Spirit (or πνεῦμα) the manner of aspirating a Syllable in pronunciation.
_{A treatise upon Greek accents [selected and] tr. from the Nouvelle methode grecque, written by the messieurs of Port Royal [really only C. Lancelot], 1729}

Montfaucon observes, that all the most ancient manuscripts, that he has met with, are written in capitals, without accents and spirits; that accents and spirits were generally introduced into manuscripts about the seventh century...
_{The Classical Journal, Volume 11, 1815}

The text throughout is loaded with interlineary accents, spirits, and musical notes. The spirits are of the antique mallet-shape, and the circumflex accent is of a reversed crescent form...
_{Universal Palaeography: Oriental writing. Greek writing. Latin writing in general, 1849}

It appears from the following definitions that in phonetics “spirit” is used with the connotation you suggest:

From Webster’s 1913 Dictionary

Spirit:

A rough breathing; an aspirate, such as the letter h; also, a mark denoting aspiration.

• (Ben Jonson) Be it a letter or spirit, we have great use for it.

and from The Chamber Dictionary :

Spiritus:

spirit, a breathing (Gr gram; spiritus asper rough breathing, spiritus lenis smooth breathing).

From Collins Dictionary

Spiritus:

(Phonetics & Phonology) a spirit or breathing