How Do I Stream Netflix Audio On A Smart TV To My AV Receiver

For $20 you can get an optical switch box.

Switch Box

With eARC you should be able to send the audio portion of your streaming content from your TV to your AVR via HDMI cable.  I'm not sure why you would want to send the video?

I'm not familiar with Anthem, but I would think any modern AVR would have an HDMI eARC input and settings to use it.  I had the same problem with an old Denon AVR.  The solution was to change the HDMI Control function.  The default setting was "OFF".  When changed to "ON" on the AVR I got audio.  Also, the LG TV remote would operate the volume on the AVR and automatically switch between the TV speakers and the surround speakers.  You probably have a similar setting if you Anthem AVR has an eARC HDMI input.

Hope this helps.
 

Click on the “audio and subtitles” menu at the top of the screen. In this menu, click on audio, and change from stereo to surround sound 5.1. Another option, if your AV receiver has the setting, is to switch it to surround sound. On most devices, this should automatically modify the setting within the Netflix app krunker

ARC, Audio Return Channel is 'magic', it works

https://www.sony.com/electronics/support/articles/00012943