I went through a lot of humidifiers for this exact issue until I landed on this guy. https://a.co/d/d9KsgV5
It’s not perfect, but it fit nearly all of my needs (which you listed above). It uses Tyua, so it’s not local UNLESS you set it up with LocalTyua like I did. The only major downside is, it beeps every time you have it do something via home assistant. If you’re crafty, you could probably remove the speaker, but I haven’t bothered (yet).
TIL you can make links to settings by long-pressing them. That’s actually awesome as hell.