Lack of eARC shouldn’t be an issue - not for DD or DD+. It sounds like the TV is having trouble pushing the data out the port - maybe check the TV settings. I suggest an Auto setting for the codec, but pass-through on the port (which shouldn’t affect the built-in apps anyway) then try powering off all devices and reseating the cable, or try a different HDMI cable. You only need to power off ‘all’ for about 30 seconds or so.. then see what happens after that. 
 

I’m assuming you do not have any other devices connected to the other HDMI ports as you haven’t mentioned any, but if there are, then perhaps switch off HDMI-CEC on those other connected devices too (if not needed).

I’d also double check the audio output settings on the Apple TV app. Some of their content for Atmos is carried via MAT, which isn’t compatible with Dolby Digital Plus, which can be carried by ARC. So making sure the app is altering the output to something proper is essential.

Thank you for the replies. I’ve looked at both the Amazon prime and Apple TV apps, and neither of them have any adjustable sound settings (I assume this would be the codec side of things?)

I seem to have fixed the Amazon prime app by toggling the TV sound setting between auto, pass-through, and PCM, such that it ended up working on auto. (I assume the tv sound setting is the HDMI port side of things?)

Bizarrely, the Sonos app is reporting a Dolby atmos (DD+) signal coming in, despite me playing an old tv show on Amazon prime that I know was only recorded in stereo. It’s as if it is ‘remembering’ the previous atmos movie I was trying to play on the Apple TV app. (Or the tv is still sending it a Dolby atmos ‘label’ if there is such a thing). 
 

The Apple TV app doesn’t work at all still - severe lip sync problem in either auto or PCM mode, and no audio at all in pass-through mode. 
 

@Tp10000 

The Digital Sound Out on the TV should normally be set to either Auto or Pass-through rather than PCM. I tend to suggest using the ‘Pass Through’ setting.

The DTV Audio Setting on the TV usually has options like Dolby Digital Plus, Dolby Digital, MPEG or HE-AAC, but there is usually an ‘Auto’ default option. I would leave that on the ‘Auto’ setting. But then perhaps also try the things mentioned in my earlier post.

See if both those settings, and suggested things mentioned previously, make things work any better for you…if not, then go back and try the Digital Sound Out set to ‘Auto’, rather than ‘Pass-Through’.

Note that the signal being sent to the Sonos does not necessarily match what the original show is in. I’ve had cases where a show originating in stereo was being sent across on a Dolby Digital carrier, so no actual signal included for the center, surrounds, or LFE channel. 
 

Edit: to be clear, it was the local station that was taking the original content in stereo and mapping it to their own Dolby Digital signal. Not an issue with my TV or Sonos.