I don't have a full answer on this.
They are certainly taken as a grammatical concept. In that they influence how the shva is sounded. Whether the shva is vocal or not.There is a slight difference in the rules on shva being vocal or not, between sephardi and ashkenazi, but both use the concept of long/short vowels as a grammatical point.e.g. https://judaism.stackexchange.com/questions/92599/what-are-the-rules-for-shva-na
There is a book "how the hebrew language grew" that around p 334 writes on this and states its opinions kind of frivously, e.g. defining it different ways without saying so explicitly, making statements he makes conflict a bit.
A thing the book says that is clear is it indicates that some people must have thought that it was longer or shorter in quantity as on p334 it quotes samuel david luzatto saying all the sephardim he hears don't distinguish kamatz gadol and patach. In the book "How The Hebrew Language Grew" p334 it says "Samuel David Luzatto, one of the most famous Hebrew Scholars of the 19th century, an Italian, wrote very simply, "All my life I grew up among Sephardic Jews, many of them distinguished scholars and rabbis. I have never heard once anyone distinguish between the ah sound of a kamatz gadol and a patah"
Another meaning of long/short is in pronunciation, like the difference between took and boot(for 'u'). bit and been(for i). Bet and bait(For 'e'). Clock(british accent not us accent), and Cloak(for 'o'). And that seems to be more to do with whether a syllable is open or closed.
And maybe some might use the term long/short to mean the vowel written in full form e.g. the 'i' vowel (chirik vowel) written with a yud following it. Vs the vowel written in its short form,so the 'i' vowel without a yud following it.
The ambiguity of the terms long/short make the terms not very good...but it's important to know the range of meanings, to try to help determine which they might mean if they sadly use the terms.
Another meaning of the concept of short vowels is how like in English, when the accent moves forward from a syllable, the vowel of the syllable lessens. Cigar becomes Cigarette. The ah of cigar equivalent to the kamatz gadol ah , becomes uh like a Hebrew shva(ashkenazim and sephardim do a shva like uh. Modern hebrew might do it like ih). .(the book "how the hebrew lanuage grew" uses that example on p337. Gadol become Gedolah or Gedolim . Maivin becomes Muhvina.