Pat, you are correct. If you select "Remote audio playback — Play on this computer," then the "Remote Audio" driver kicks in on the host machine, and it disables all other audio devices connected to the host and makes them disappear. I am pretty sure RDP is designed this way on purpose, and there is simply no way to hear the host's audio on both machines at the same time. I beat my head against the wall with all of the registry tweaks and group policy settings that you see online about RDP audio, for literally a couple of years, to figure out whether there is a way to tell RDP to allow microphones attached to a host machine to continue to be visible to applications running on the host while at the same time sending their output to me remotely, but there isn't any. To do that, you need to switch to another product such as AnyDesk.
I came up with a workaround, however. If you are still following this question, let me know and I can describe it. It involves setting up a second computer next to your host, sending your host's audio to it, and then logging into both remote machines at the same time using two separate instances of RDP on your local client. You watch the video on one of them, and you listen to the audio on the other one.
Jerry