Thanks for your response. see my response italicized.
APPLE TV AND DISNEY +
APPLE TV TO A16 TO TV TO START WITHOUT SPLITTER. WITH SPLITTER, TRIED BEFORE THE A16 AS WELL AS AFTER.
Naturally I don't subscribe to either. So I can't duplicate your experience exactly.
But I can say that using Netflix on my ATV4K 2019, with ATV4K -> A16 -> LG OLED C9 (audio output set to HDMI-ARC, not that it should be relevant) I show DV+DA on the Netflix poster page for the movies. And when I play them, the A16 starts off briefly showing PCM but then changes to Dolby Atmos. And I'm definitely getting getting Atmos audio.
I did power up the A16 first, and selected my preset for ATV4K with 15.1.8 Atmos Audio listening room. Then I powered on the ATV4K, which also caused the TV to power on (because of HDMI-CEC being active on all my devices). Then navigated to Netflix on ATV4K, selected a movie known to have DV+DA (and both showed on the info poster), pushed PLAY, and shortly thereafter the A16 display screen showed audio being received, first as PCM briefly but then it changed to Dolby Atmos. TV audio is still at "HDMI-ARC" as it should be (not that this is relevant).
Back on the ATV4K video settings, my video format is "4K Dolby Vision 60 (59.94hz)". Match Content items are both ON (Match Dynamic Range, Match Frame Rate).
And my ATV4K "audio output" setting is "Default audio output -> TV speakers", not that I use them since sound is coming through the A16 and headphones and no audio is actually coming out of the A16, only video. And besides my LG C9 is currently set to HDMI-ARC so its speakers are not really activated anyway.
ATV4K "audio format" shows as "Auto, Atmos Available". Settings are "Change format -> OFF" (so as NOT to get LPCM) and Immersive Audio -> Dolby Atmos -> ON".
That's about the best I can offer, not having the two streaming source apps you're fighting with.