Some apps on the apple tv still have ads on the pause screen (covering the content I may have wanted to pause to see, a terrible UX choice). It can't be entirely avoided.

It can if you avoid a dedicated device and just hook a desktop up to your TV. It's a one time cost to set up a host you control and that seems to be getting more and more worth it.

Is there a solution for audio and video downscaling when accessing content via the browser in a linux htpc setup?

I don't think any of the big streaming content providers have native apps on linux and no browser can pass through audio bitstreams to HDMI. Video quality is limited as well.

Having a dedicated streaming box is better in this regard