OK, I did web searches for both. Yes, the projector supports HDR. However, after searching numerous sites, including the Denon product page, the term HDR doesn't appear in any of them. That seems far too odd to simply be something that the reviewers overlooked. I did find it mentioned on one review, but it's really odd the Denon page makes no mention of it.
I have a hunch your AVR isn't supporting it, and your Firestick is simply ignoring the lack of support. I know when I replaced my family room TV with an LG that supports Dolby Vision, I had to swap my two Yamaha AVRs because the one in the bedroom supported DV while the other only supported HDR.
Beyond that, you might look in the Denon owners manual to see if there's a setting for the HDMI ports to enable High Color, UHD Color, or some other designation that might indicate HDR support. I have to do the same in my TVs, so perhaps the projector has it as well. Samsung calls it UHD Color, LG calls it HDMI Ultra HD Deep Color, and other brands have different names. But they all need to be enabled to permit HDR/DV on the display. Otherwise the HDMI port doesn't have the speed capacity to support 4K/HDR content.
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