No HDMI Audio on NUC10i3FNK with HP 24ea Display

If you install and use pavucontrol does it help?

No, pavucontrol only lists the "Dummy Device". The configuration tab is empty.

Some additional information

$ lspci -vv | grep -A2 Audio
00:1f.3 Audio device: Intel Corporation Device 02c8
 Subsystem: Intel Corporation Device 2081
 Control: I/O- Mem+ BusMaster+ SpecCycle- MemWINV- VGASnoop- ParErr- Stepping- SERR- FastB2B- DisINTx+

$ inxi -Fv 6
System: Host: ub Kernel: 5.8.0-59-generic x86_64 bits: 64 compiler: N/A Desktop: Gnome 3.36.9 wm: gnome-shell dm: GDM3
           Distro: Ubuntu 20.04.2 LTS (Focal Fossa)
Machine: Type: Mini-pc System: Intel Client Systems product: NUC10i3FNK v: M38061-307 serial: <superuser/root required>
           Chassis: Intel Corporation type: 35 v: 2.0 serial: <superuser/root required>
           Mobo: Intel model: NUC10i3FNB v: M38070-306 serial: <superuser/root required> UEFI: Intel
           v: FNCML357.0052.2021.0409.1144 date: 04/09/2021
[...]
CPU: Topology: Dual Core model: Intel Core i3-10110U bits: 64 type: MT MCP arch: Kaby Lake rev: C L2 cache: 4096 KiB
           flags: avx avx2 lm nx pae sse sse2 sse3 sse4_1 sse4_2 ssse3 vmx bogomips: 20799
           Speed: 700 MHz min/max: 400/4100 MHz Core speeds (MHz): 1: 700 2: 700 3: 700 4: 700
Graphics: Device-1: Intel UHD Graphics driver: i915 v: kernel bus ID: 00:02.0 chip ID: 8086:9b41
           Display: x11 server: X.Org 1.20.9 driver: i915 compositor: gnome-shell resolution: 1920x1080~60Hz
           OpenGL: renderer: Mesa Intel UHD Graphics (CML GT2) v: 4.6 Mesa 20.2.6 direct render: Yes
Audio: Device-1: Intel driver: snd_hda_intel v: kernel bus ID: 00:1f.3 chip ID: 8086:02c8
           Sound Server: ALSA v: k5.8.0-59-generic
[...]

$ aplay -l
**** Liste der Hardware-Geräte (PLAYBACK) ****

$ aplay -L
default
    Playback/recording through the PulseAudio sound server
surround21
    2.1 Surround output to Front and Subwoofer speakers
surround40
    4.0 Surround output to Front and Rear speakers
surround41
    4.1 Surround output to Front, Rear and Subwoofer speakers
surround50
    5.0 Surround output to Front, Center and Rear speakers
surround51
    5.1 Surround output to Front, Center, Rear and Subwoofer speakers
surround71
    7.1 Surround output to Front, Center, Side, Rear and Woofer speakers
null
    Discard all samples (playback) or generate zero samples (capture)
samplerate
    Rate Converter Plugin Using Samplerate Library
speexrate
    Rate Converter Plugin Using Speex Resampler
jack
    JACK Audio Connection Kit
oss
    Open Sound System
pulse
    PulseAudio Sound Server
upmix
    Plugin for channel upmix (4,6,8)
vdownmix
    Plugin for channel downmix (stereo) with a simple spacialization
surround21:CARD=PCH
    2.1 Surround output to Front and Subwoofer speakers
surround40:CARD=PCH
    4.0 Surround output to Front and Rear speakers
surround41:CARD=PCH
    4.1 Surround output to Front, Rear and Subwoofer speakers
surround50:CARD=PCH
    5.0 Surround output to Front, Center and Rear speakers
surround51:CARD=PCH
    5.1 Surround output to Front, Center, Rear and Subwoofer speakers
surround71:CARD=PCH
    7.1 Surround output to Front, Center, Side, Rear and Woofer speakers
usbstream:CARD=PCH
    HDA Intel PCH
    USB Stream Output

$ cat /etc/modprobe.d/alsa-base.conf
# autoloader aliases
install sound-slot-0 /sbin/modprobe snd-card-0
install sound-slot-1 /sbin/modprobe snd-card-1
install sound-slot-2 /sbin/modprobe snd-card-2
install sound-slot-3 /sbin/modprobe snd-card-3
install sound-slot-4 /sbin/modprobe snd-card-4
install sound-slot-5 /sbin/modprobe snd-card-5
install sound-slot-6 /sbin/modprobe snd-card-6
install sound-slot-7 /sbin/modprobe snd-card-7

# Cause optional modules to be loaded above generic modules
install snd /sbin/modprobe --ignore-install snd $CMDLINE_OPTS && { /sbin/modprobe --quiet --use-blacklist snd-ioctl32 ; /sbin/modprobe --quiet --use-blacklist snd-seq ; }
#
# Workaround at bug #499695 (reverted in Ubuntu see LP #319505)
install snd-pcm /sbin/modprobe --ignore-install snd-pcm $CMDLINE_OPTS && { /sbin/modprobe --quiet --use-blacklist snd-pcm-oss ; : ; }
install snd-mixer /sbin/modprobe --ignore-install snd-mixer $CMDLINE_OPTS && { /sbin/modprobe --quiet --use-blacklist snd-mixer-oss ; : ; }
install snd-seq /sbin/modprobe --ignore-install snd-seq $CMDLINE_OPTS && { /sbin/modprobe --quiet --use-blacklist snd-seq-midi ; /sbin/modprobe --quiet --use-blacklist snd-seq-oss ; : ; }
#
install snd-rawmidi /sbin/modprobe --ignore-install snd-rawmidi $CMDLINE_OPTS && { /sbin/modprobe --quiet --use-blacklist snd-seq-midi ; : ; }
# Cause optional modules to be loaded above sound card driver modules
install snd-emu10k1 /sbin/modprobe --ignore-install snd-emu10k1 $CMDLINE_OPTS && { /sbin/modprobe --quiet --use-blacklist snd-emu10k1-synth ; }
install snd-via82xx /sbin/modprobe --ignore-install snd-via82xx $CMDLINE_OPTS && { /sbin/modprobe --quiet --use-blacklist snd-seq ; }

# Load saa7134-alsa instead of saa7134 (which gets dragged in by it anyway)
install saa7134 /sbin/modprobe --ignore-install saa7134 $CMDLINE_OPTS && { /sbin/modprobe --quiet --use-blacklist saa7134-alsa ; : ; }
# Prevent abnormal drivers from grabbing index 0
options bt87x index=-2
options cx88_alsa index=-2
options saa7134-alsa index=-2
options snd-atiixp-modem index=-2
options snd-intel8x0m index=-2
options snd-via82xx-modem index=-2
options snd-usb-audio index=-2
options snd-usb-caiaq index=-2
options snd-usb-ua101 index=-2
options snd-usb-us122l index=-2
options snd-usb-usx2y index=-2
# Ubuntu #62691, enable MPU for snd-cmipci
options snd-cmipci mpu_port=0x330 fm_port=0x388
# Keep snd-pcsp from being loaded as first soundcard
options snd-pcsp index=-2
# Keep snd-usb-audio from beeing loaded as first soundcard
options snd-usb-audio index=-2

#options snd-hda-intel single_cmd=1
#options snd-hda-intel probe_mask=1
#options snd-hda-intel model=basic

$ alsactl init
alsa-lib main.c:1021:(snd_use_case_mgr_open) error: failed to import hw:0 (empty configuration)
Found hardware: "HDA-Intel" "Intel Kabylake HDMI" "HDA:8086280b,80860101,00100000" "0x8086" "0x2081"
Hardware is initialized using a generic method

$ head -n 1 /proc/asound/card0/codec#2
Codec: Intel Kabylake HDMI

$ dmesg | egrep -i "alsa|snd|hdmi"
[ 0.139020] ACPI: Added _OSI(Linux-Lenovo-NV-HDMI-Audio)
[ 4.085278] snd_hda_intel 0000:00:1f.3: enabling device (0000 -> 0002)
[ 4.169438] snd_hda_intel 0000:00:1f.3: bound 0000:00:02.0 (ops i915_audio_component_bind_ops [i915])
[ 4.456807] snd_hda_codec_hdmi hdaudioC0D2: HDMI: pin nid 5 not registered

$ cat /proc/asound/cards
 0 [PCH ]: HDA-Intel - HDA Intel PCH
                      HDA Intel PCH at 0x6023110000 irq 156

$ pacmd list-cards
0 card(s) available.

$ pacmd list-sinks
1 sink(s) available.
  * index: 0
 name: <auto_null>
 driver: <module-null-sink.c>
 flags: DECIBEL_VOLUME LATENCY DYNAMIC_LATENCY
 state: RUNNING
 suspend cause: (none)
 priority: 1000
 volume: front-left: 65536 / 100% / 0,00 dB, front-right: 65536 / 100% / 0,00 dB
         balance 0,00
 base volume: 65536 / 100% / 0,00 dB
 volume steps: 65537
 muted: no
 current latency: 0,12 ms
 max request: 0 KiB
 max rewind: 0 KiB
 monitor source: 0
 sample spec: s16le 2ch 44100Hz
 channel map: front-left,front-right
              Stereo
 used by: 2
 linked by: 2
 configured latency: 0,50 ms; range is 0,50 .. 2000,00 ms
 module: 14
 properties:
  device.description = "Dummy-Ausgabe"
  device.class = "abstract"
  device.icon_name = "audio-card"

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