No sound after fresh install - XFCE / Alder Lake / Multiple kernel versions

Replacing PulseAudio with PipeWire is not likely to help resolve an issue in ALSA

The warning about missing folder /etc/pulse/default.pa.d is not a problem and can be ignored

PulseAudio 15.0 Release notes - The startup script can now read additional configuration from the /etc/pulse/default.pa.d/ directory
there is now an include directive that loads files from /etc/pulse/default.pa.d/ or /etc/pulse/system.pa.d/. This is primarily meant for distributions when they want to add some module to the configuration when installing a package

One simple way to stop the warning messages is create an empty folder

sudo mkdir -p /etc/pulse/default.pa.d

(The new configuration in /etc/pulse/default.pa can be edited to disable/remove .include /etc/pulse/default.pa.d but this will need additional maintenance when PulseAudio updates create a .pacnew file)

See this post for how to deal with warning about battery level indicator:

Problem with Bluetooth audio is unlikely to affect onboard analog audio

I was hoping to see something about why PulseAudio data is showing ALSA using Skylake driver snd_soc_skl_hda_dsp instead of sof-audio-pci-intel-tgl in inxi data
hardware scans for previous generations of Elitebook 840 and current HP Alder lake models all use the tgl Tiger lake driver

I suggest you get more information about ALSA with this command

sudo alsa-info.sh --upload

and post the link to uploaded data here