Pulseaudio does not connect to snd_hda_intel

Since approximately version 20.04 pulseaudio has failed to include the analog sound options in its configuration settings for the series 6 c200 chipset. Meaning that it is impossible to use either built in or external speakers without using either bluetooth (which has its own problems) or USB (which uses up USB sockets).

ProblemType: Bug
DistroRelease: Ubuntu 22.04
Package: pulseaudio 1:15.99.1+dfsg1-1ubuntu2.1
ProcVersionSignature: Ubuntu 5.15.0-76.83-generic 5.15.99
Uname: Linux 5.15.0-76-generic x86_64
ApportVersion: 2.20.11-0ubuntu82.5
Architecture: amd64
AudioDevicesInUse:
 USER PID ACCESS COMMAND
 /dev/snd/controlC0: mark 1565 F.... wireplumber
 /dev/snd/seq: mark 1564 F.... pipewire
CasperMD5CheckResult: unknown
CurrentDesktop: XFCE
Date: Mon Jul 3 19:55:46 2023
InstallationDate: Installed on 2023-06-30 (3 days ago)
InstallationMedia: Xubuntu 20.04.3 LTS "Focal Fossa" - Release amd64 (20210819.1)
ProcEnviron:
 LANGUAGE=en_GB:en
 PATH=(custom, no user)
 XDG_RUNTIME_DIR=<set>
 LANG=en_GB.UTF-8
 SHELL=/bin/bash
PulseList: Error: command ['pacmd', 'list'] failed with exit code 1: No PulseAudio daemon running, or not running as session daemon.
SourcePackage: pulseaudio
UpgradeStatus: Upgraded to jammy on 2023-06-30 (3 days ago)
dmi.bios.date: 03/12/2015
dmi.bios.release: 15.96
dmi.bios.vendor: Hewlett-Packard
dmi.bios.version: 68SCF Ver. F.60
dmi.board.name: 161C
dmi.board.vendor: Hewlett-Packard
dmi.board.version: KBC Version 97.4E
dmi.chassis.type: 10
dmi.chassis.vendor: Hewlett-Packard
dmi.ec.firmware.release: 151.78
dmi.modalias: dmi:bvnHewlett-Packard:bvr68SCFVer.F.60:bd03/12/2015:br15.96:efr151.78:svnHewlett-Packard:pn:pvrA0001C02:rvnHewlett-Packard:rn161C:rvrKBCVersion97.4E:cvnHewlett-Packard:ct10:cvr:sku:
dmi.product.family: 103C_5336AN
dmi.product.version: A0001C02
dmi.sys.vendor: Hewlett-Packard