My first thought here is that tools for hunting would probably involve stone/flint, formed in some way, indicating to archeologists that they were tools of some sort, whereas digging sticks for foraging tubers etc were, in fact, sticks, and not likely to stick around long enough for an archeologist to discover.
Cave paintings were most likely done by men - maybe not, but likely a higher status occupation for a higher status person, ie male. History written by the conqueror (or stronger, more dominant): men hunted, men painted, hunting got preference in the paintings. Also, hunting would have been more dangerous; bringing down a mammoth would have had more “story value” than filling a basket with hazelnuts.
Hunted animal residue would include (almost exclusively after so many millennia) bones, which fossilize. Leftover wild strawberries not so much.
Just a few thoughts, not arguments. My hunch is that greater value was likely put on meat, but the veggie/fruit gathering was a helpful adjunct, especially when the hunting didn’t go well.