You should be able to use the Shield remote to control a) apps on the Shield, b) power and volume on the Denon and TV.
Part of the HDMI specification includes HDMI-CEC, which controls power and volume.
My setup: Shield ā HDMI ā Denon ā HDMI-ARC ā LG B7 OLED
When I press the power button on my Shield remote it powers on all three devices and switches the TV to HDMI2, the interface connected to the Denon.
Volume up/down on the Shield remote controls the volume on my Denon receiver.
This works quite well with the Plex, YouTube TV, and other apps on the Shield.
My Shield is the 2015 model, which does not support Dolby Vision. Because of this I use the LG TV apps for Netflix and Amazon, since they support Dolby Vision. The Plex app on the current Shield will direct play Dolby Vision video. I do not know if the Netflix & Amazon apps on the current Shield support Dolby Vision.
The LG remote will also control volume up/down and power on/off on the Denon receiver. I do not know if it will control apps on the Shield. Iāve never tried.
Bottom line, 99% of my media consumption is with four apps: Plex, YouTube TV, Netflix, and Amazon. I use both the Shield and LG remotes. If my Shield supported Dolby Vision I would be down to just the Shield remote.
I use the Shield for Plex and YouTube TV. I press the power button on the Shield remote. It powers on the Shield, Denon, and TV and switches the TV to the correct HDMI input. I use the Shield remote to control the apps.
I use the LG TV apps for Netflix and Amazon. I press the Netflix or Amazon button on the LG remote. It powers on the TV and Denon, switches the Denon to receive audio from the TV, and launches the appropriate app. I use the LG remote for volume up/down, forward/rewind, etc.