I use a Mammotion Mini for my backyard which I got at a pretty big discount during Memorial Day sales. I don't have HA, but it seems there's some work going on for integration: https://community.home-assistant.io/t/mammotion-luba-integration/604662/63.

It does require internet access though, and I put it in my isolated guest vlan to be safe. I haven't tried running it without an internet connection yet. Obviously this doesn't meet all your requirements, but I can at least attest that the mower itself is pretty good. Good luck on your search!

My neighbor has one. It seems to do a decent job cutting the grass and hasn't mulched their dog yet.

I have 0.2 acres with a Husqvarna auto mower.

Frankly I don't really "manage" it, it just mows and occasionally I get a notification if it gets stuck or something.

So I haven't really had reason to care about HA or Internet monitoring of it, though it does have a feature to park off it has internet module and forecast shows rain.

But anyway, mine requires a boundary wire and that breaks and is really annoying. I'd hope a wire free solution works well by now.