Thank you. This link (https://discovery.endeavouros.com/audio/pulseaudio/2021/12/) helped me solve the issue. I almost did not get past not being able to remove a crucial depency breaking package gnome-bluetooth-3 and 3.0 (hence “–nodeps --nodeps”).
Here are the commands that were required get sound for my computer (an Intel Nuc 12 with sound through hdmi cable):
$ sudo pacman -R --nodeps --nodeps gnome-bluetooth-3
$ sudo pacman -R --nodeps --nodeps gnome-bluetooth-3.0
$ sudo pacman -S pulseaudio
$ sudo pacman -S pulseaudio-alsa pulseaudio-jack pulseaudio-bluetooth
$ systemctl --user stop pipewire-pulse.service
$ systemctl --user start pulseaudio
$ inxi -Aaz
# + a reboot was required in the end