At least that's what German Wikipedia Claims while the corresponding paragraph in english Wikipedia is short.
[1] https://vitrinelinguistique.oqlf.gouv.qc.ca/fiche-gdt/fiche/... [2] https://www.noslangues-ourlanguages.gc.ca/fr/cles-de-la-reda...
EDIT: "Creation of Computer Input in an Expanded Character Set" at https://ejournals.bc.edu/index.php/ital/article/download/292... from 1968, p112, describes it simply as "at".
EDIT #2: "TRANSLATION FROM MONOTYPE TAPE TO GRADE 2 BRAILLE" at p83 of https://archive.org/details/researchbulletin05lesl/page/82/m... from 1964 describes that symbol as the '"at" sign'.
I think that is early enough to say that email did not influence the "at" meaning but rather the other way around.
What I can't find is when it was first used in the US for indicating home-team for sports. E.g. [1] where there is vs. or @ depending on whether it is a home or away game. I suspect it's relatively modern, but not sure how far back it goes.