I have the Roam Wild Pest Off feeder hanging from a tree in one of my runs. It is true that rodents and large birds cannot feed from it, but the sparrows can land on the feed opening and even on the little button that closes the opening when a rodent gets on it, and they feed very happily. A flock of them could empty the feeder in a day or two. I was disappointed about that and wish I could think if a way to make the "trigger button" (for lack of a better description) more sensitive to exclude sparrows as well. It looks like the birdie Berlin Airlift out there some days...https://homgar.com/products/rat-proof-chicken-feeder
Here's a couple examples. You can put a baffle or disc on the post and make the post out of smooth metal so the squirrels can't climb it. Rats can climb too. Rats climb extremely well.
Hardware cloth across the whole bottom small enough to stop rodents will keep chickens from eating the grass and scratching. Keep anything suspended at least a rat length off the ground (so maybe 10"-1'?) and 2' away from any walls. Still, these can be picked up and moved with relative ease.