Resolved. I couldn't get multichannel sound from my Oppo BR player. It turns out that unless I turn off my receiver the Oppo only outputs (from its second output?) in stereo, which is probably a by-product of using both HDMI outputs from the Oppo simultaneously.
I do NOT use the HDMI pass-through of the A16 when using my Oppo 203. The A16 is simply fed from HDMI2-out (audio-only), and the A16 is powered on when I want to use my headphones.
HDMI1-out of the 203 goes to my AVR, to provide video-only when the A16 is powered on, and then HDMI-out of the AVR goes to the TV. When the A16 is powered off HDMI1-out carries both audio and video to the AVR, so that the speakers (managed by the AVR) are heard.
The 203 is configured Setup Menu -> Audio output setup -> HDMI audio format. For all non-Atmos multi-channel (e.g. 5.1 or 7.1, lossy or lossless, Dolby or DTS) audio (either from a disc played by the Oppo, or from an HDMI external input source feeding the Oppo such as HDTV DVR or Roku etc.) you might as well set HDMI audio format to LPCM. This lets the Oppo perform all audio decoding upstream to the A16 for any audio format (including DTS) and feed 2.0/5.1/7.1 audio as LPCM to the A16 (via HDMI2-out of the Oppo when you have the A16 powered on). This will be handled by the A16 through a "PCM room" and will work perfectly. When the A16 is powered off the decoded multi-channel LPCM audio will be fed along with video through HDMI1-out of the Oppo to your AVR, so that you can listen to multi-channel sound through the multiple speakers managed by the AVR..
For Atmos output from a disc played by the Oppo, reconfigure Audio Output Setup -> HDMI audio format to BITSTREAM. Now the audio output from HDMI2-out of the Oppo will carry the still-decoded Dolby Atmos audio to the A16, where it will be handled by the A16 through an "Atmos room". If the A16 is powered off the Atmos BITSTREAM audio will be sent along with video out of HDMI1-out of the Oppo, to your AVR for decoding there.
Note specifically that Roku (Ultra) streamer does NOT support either Dolby Vision nor Dolby Atmos from its apps. It does support UHD 4K (HDR) but not Dolby Vision. And it only supports multi-channel audio but not Dolby Atmos. I have a Roku Ultra and I feed it as one external HDMI source into an HDMI SWITCH which in turn feeds its HDMI-out to HDMI-in of the Oppo, which in turn feeds 5.1/7.1 audio through HDMI2-out to the A16. I also feed my cable TV DVR as a second external HDMI source into the same HDMI SWITCH, so that conventional Dolby Plus 2.0/5.1 surround sound from HDTV is also fed through the HDMI switch to the Oppo and on to the A16. For listening to both of these external HDMI sources through the Oppo I have HDMI audio format on the Oppo set to LPCM.
Note that HDMI1-out of the Oppo goes to HDMI1-in of my AVR.
In contrast, the Apple TV 4K streamer DOES SUPPORT BOTH Dolby Vision as well as Dolby Atmos from its apps (assuming the apps themselves support these Dolby licensed features, as the Netflix app does on ATV4K). I have tried passing the ATV4K as a third input through the same HDMI switch (already set to accept both Roku and DVR) and then out of the switch and on to the Oppo HDMI-in (and then bitstream audio through HDMI2-out of the Oppo to the A16), but my own experience is that this is very problematic. The HDMI handshakes involved with all of the devices seems to produce either delays, or unreliable results, or the Oppo automatically switching to LPCM (even though I've set it to BITSTREAM), or just general confusion and failure.
So specifically for my ATV4K I feed it directly to HDMI2-in of the A16 (where it is handled as an "Atmos room" in order to decode all bitstream Dolby audio from the ATV4K, both Dolby Atmos as well as non-DA). And I have HDMI-out of the A16 (pass-through) going to a second HDMI2-in on my AVR. This supports ALL AUDIO FORMATS coming from the ATV4K provided as BITSTREAM to the A16, while video (both Dolby Vision as well as non-DV) comes from the ATV4K and passes through the A16 and then on to the AVR to feed the HDTV. Note that I've got the Oppo HDMI2-out feeding HDMI1-in of the A16 (where it is the "end of the line" for audio when using the A16). So any direct or external A/V source coming from the Oppo feeds audio to the A16, and audio/video to the AVR through one of its HDMI inputs. For A/V from the ATV4K audio+video goes to the A16 and then video-only goes through the A16 and on to a second HDMI input of the AVR.
Yes, I do have to switch my AVR to use its second HDMI2-in specifically when watching something from ATV4K as the source (passing through the A16). All Oppo-related source uses HDMI1-in of the AVR. But this approach absolutely provides reliable and consistent results for ATV4K-provided Dolby Vision and Dolby Atmost content. I also happen to prefer the GUI user-interface and physical remote user-friendliness of the Roku, so for all streaming service apps which are present on both Roku and ATV4K I will always use Roku (and by inference, also through the Oppo with video output to the AVR and audio output LPCM to the A16) as long as I'm not losing DV or DA. I only use ATV4K (directly bitstream to the A16 and then HDMI-out of the A16 to a second HDMI input of the AVR) when the source content is DV and/or DA.