It turns out that after following the below guide, I found that another package
called timidity is conflicting with PulseAudio and causing it to fail detecting
my audio devices.
So I uninstalled it and PulseAudio is now working fine.
sudo apt-get remove timidity
Public bug reported:
[HP Pavilion dv6 Notebook PC, IDT 92HD75B3X5, Speaker, Internal]
Pulseaudio fails to detect card
ProblemType: Bug
DistroRelease: Ubuntu 21.10
Package: pulseaudio 1:15.0+dfsg1-1ubuntu2
ProcVersionSignature: Ubuntu 5.13.0-21.21-generic 5.13.18
Uname: Linux 5.13.0-21-generic