but the table exists outside the alt text, right? i don't know a mechanism to say "this html table represents the contents of this image" , in a way that screen readers and other accessibility technologies take advantage of

The figure tag has both image and caption tags that link them. As far as I remember, some content could be marked as screen reader only if you don't want for the table to be visible to the rest of the users.

Additionally, recently I've been a participant in accessibility studies where charts, diagrams and the like have been structured to be easier to explore with a sr. Those needed js to work and some of them looked custom, but they are also an alternative way to layer data.