You're right, specs vary online.
This one has a rating of 70w into 4 ohms.
https://www.cnet.com/news/low-costhigh-performance-contender-onkyo-a-9010-integrated-amplifier/I think the real issue is that the Kappa's are more demanding than a 4 ohm speaker. I dont see an impedance curve which would show how often there is a demand for high power/current.
The Onkyo will certainly drive your speakers, but you may be missing out on detail and texture in the bass frequencies. It's possible that the speaker's demand during peaks and transients may push the amp into clipping, which is distortion.
With this combo you are at the very minimum of what the speakers demand. Have you looked at the next model up the ladder?, I forget the model number.