The "pastekodi" command is probably failing due to the size of the log (limits on the paste server are generous, but there are limits) and the Kodi log is zero value because it's captured hours after boot, so it has rotated and useful info shown during initial startup is no longer present. It also looks like you copy/pasted from a terminal session as some text is truncated (not a major thing..).
The OS seems to have an issue with the iwlwifi card as this is throwing errors. Not sure it's too important but it adds to the log noise and might indirectly impact on other aspects of boot. Nothing else really stands out to me.
However, audio capabilities in Kodi are determined from EDID data on the HDMI connection at startup. If Kodi cannot see/find audio hardware either the kernel doesn't detect it, correctly or (more likely in this case) something is messing with EDID data.
I'll make an educated guess that the HDMI output spec from the NUC is not aligned to the HDMI spec of the input on the AVR, e.g. something like the NUC only supporting 4:2:0 and the AVR requiring 4:2:2. It reads a little like you picked "the best port" for input on the AVR but instead of ensuring best results this could be counter-productive and you might need to swap to another (lesser) input port or experiement with changes to the HDMI spec support of the port to make things work. I'm being a little vague about things here because different vendors name things differently. The important thing to understand is that HDMI is a collection of standards (interpreted by vendors) not 'a' standard.
I would also experiment with cables (only use HDMI 2.0 certified ones) and the second HDMI port on the NUC, and also external DP to HDMI adapters instead of the HDMI output sockets on the NUC. The reason being that most NUC like boxes omit proper HDMI transciever hardware to save $$ and instead uses an internal DP to HDMI adapter (aka LSPCON chip) which contains closed-source firmware doing magic and imposing unseen limitations on the display chain - they are often oriented towards output on monitors more than TV's. Make sure the BIOS/firmware of the NUC and if separate any LSPCON firmware updates are applied as they can/do contain bugs. The advantage of external DP > HDMI adapters is that they aren't soldered to the motherboard inside the box so you can order a bunch of different ones and experiment until you find one that works. NB: There is also a long-running 'Denon AVR' thread elsewhere in the forums that you can read, but IIRC the main conclusion of that thread is people ditching the internal HDMI ports for external DP > HDMI adapters. The tertiary challenge is that different brands of adapters are available in different parts of the world, and even if the same brand is available there's no guarantee the LSPCON chip and firmware inside the latest batch of adapters is the same as the chip and firmware that someone tested a year ago and worked great. LSPCON chips in NUC boxes has been "the gift that keeps on giving" for HDMI support issues since they first appeared 6-8 years ago.
Note to self .. I should scrape this text ^ into a wiki article, it's not the first time I had to write it all out long-hand 
