There seem to be no necroposting rules here.
I had two headcanons that addressed this, although I'm not sure which one I prefer. I interpret "sentient" as human-equivalent ability to learn language, think, and create, so sentient Pokemon will be able to talk, build villages/towns/etc, and create writing systems and other tools.

A) Not all pokemon are sentient. Similar to the varying levels of intelligence in the animal world, Pokemon have varying levels of sentience. Alakazam and Metagross are very intelligent, for example, while Hydreigon is not sentient and runs around in a bind rampage unless it is trained. Sentient Pokemon and humans may look down on non-sentient Pokemon and eat them.

B) All Pokemon are sentient; this doesn't prevent them from killing and eating each other, hunting humans, or being hunted, farmed and bred by humans. While many Pokemon are peaceful and don't look to attack humans, others can and do and this is why people are warned not to head into wild areas without a buddy of their own.

• A few species are well known for their past brutality towards humans and have a habit of trying to carry it out (Deino, Litwick)
• A few species are friendly towards humans and enjoy helping them and collaborating (the starters, Miltank, Pokemon like Ralts)
• Most species are neutral - they don't lean either way.

Humans need to make sure to maintain strong relationships with members of neutral Pokemon species to make sure they don't get attacked. This also benefits the neutral Pokemon, since they also do not want to be hunted down by humans.

This thread addresses the eating habits of humans, however.

In situation A) non-sentient Pokemon are farmed and bred by humans and sentient Pokemon. This means that their situation is analogous to our world.

In situation B) farming is not possible in the traditional sense. Instead, Miltank might be willing to share their milk and Chansey would voluntarily give you its eggs. Perhaps farmers meet a herd who is willing to share with them, and that is how "farms" are set up.
More violent humans/Pokemon will have to go and hunt their prey. This is time consuming and unreliable, which explains why humans rely much more on plants for food. In the modern Pokemon world, hunting is seen as unnecessary due to advances such as lab-grown meat and the perception that hunting Pokemon might instigate attacks against humans. However, there is a demand for hunted meat, particularly in luxury hotels and so on, which fuels people to become hunters if they want to make a bit of cash.

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