Ye olde sieges cut off supply lines and forced the defenders to subsist on rations. Once those started running low, they started starving. Eventually the options were starve to death or surrender. These sieges frequently lasted months and sometimes years. Given travel times, it could also be weeks before anyone realized something was wrong and mobilized a force to break the siege.
Ukraine can only do infrequent drone raids. In order to properly siege Moscow, they would need to lock down all ways in and out of the city, and keep it that way for months, possibly longer given modern food preservation techniques and the viability of backyard farming. Additionally, sieging a city no longer prevents the people from communicating with the outside world, meaning other Russian forces would respond in days.
Other than the cooking thing, which is more us understanding it’s better for us than a hard requirement, humans are actually amazing omnivores. Dogs and wolves are some of our closest competitors there and we’re still miles ahead.