I have a Sony STR-DH820 A/V Receiver, Is it compatible with the Apple TV 4K?

You receiver has HDMI 1.x ports (with HDCP 1.x), with aren’t sufficient for (commercial) 4K content. The alternative is to consider upgrading to an AV receiver with HDMI 2.0 (with HDCP 2.2) or even better HDMI 2.1 ports (with HDCP 2.3).

Such is the way of modern electronics. In 2011, the HDCP 2.2 specification was still three years away. No way to support that in advance.

You may want to consider upgrading your receiver. I did this a few years ago when I got my Apple TV 4K. There a lot of receivers available these days that support video passthrough and a LOT of other new features you can take advantage of in a variety of price ranges.

The receiver I ended up with was an Onkyo TX NR686 which has since been upgraded. I think I paid $349 for it from Amazon.

Video passthrough via the older receiver would be limited to 1080p.

Instead, consider: Apple TV →[HDMI]→ TV →[HDMI ARC]→ receiver

with audio passthrough via the TV.

Your welcome and good luck!