Ah - I just found this on mine:
You can’t go below a 0.5 degrees C delta, but the RH can be set to a delta of 1% RH. So set that and see if you get better behaviour in HA.
Oddly enough I’ve just updated to beta firmware 0.13.0-beta1 - it offered it to me for some reason and now it’s offering me 0.12.0 again.
So some oddness going on there too. I don’t see many changes anyway in 0.13.0.