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I don't think there are any 'normal' animals around any more, honestly. There may have been some in the past, and so you get references to them in some dex entries, but they seem entirely absent now. Omnivores and carnivores, therefore, probably eat other Pokemon (which makes it problematic, given that they're more than likely sapient). There may be a higher-than-usual degree of herbivorism, though (especially since there seems to be no shortage of non-sapient or sentient plants), or true carnivorism is rare in favor of omnivorism - all Pokemon can eat berries, for instance, and things like poffins and pokeblocks (made from berries). Therefore, a plant-based diet may be more common.
There are, of course, Pokemon who eat non-biological things like minerals (hi, Sableye!), and some that just eat weird shit like 'life energy'. And a fair few Grass types may photosynthesize - the Hoppip line, for instance, or the Cherubi line. (Others, especially more animal-based ones like Torterra or Sawsbuck, may supplement their diets with other stuff, probably non-sentient plants.)
Pokemon who have been caught may have commercial Pokemon food, which may not necessarily contain slaughtered Pokemon so long as it has all the required nutrients.
