The following sort of investigation is what comes to mind for the issue.
In the alsa-info output it says:
!!Sound Servers on this system
Installed - Yes (/usr/bin/pipewire)
Running - Yes
No sound servers found.
Presumably pipewire is installed, but not operating as intended.
You could check to see what is controlling or commanding your sound card with:
On this machine I'm writing from the output is:
COMMAND PID USER FD TYPE DEVICE SIZE/OFF NODE NAME
pulseaudi 1055 flop mem CHR 116,11 539 /dev/snd/pcmC0D0p
pulseaudi 1055 flop 16u CHR 116,16 0t0 554 /dev/snd/controlC0
which shows pulseaudio as the sound server being used.
You can check that info also with:
and it should give the same result as the lsof command.
Since you are running an Intel sound card, you likely need to have the intel sound firmware installed. It's a package that's usually named: firmware-intel-sound. If it's not installed, install it and see if it makes a difference.
Next thing to check is whether sound has been muted, so run:
and press F5, to see all the volume controls. Press F1 to see the help commands. if needed. If anything is muted, it's indicated by the letter M at the base of the bars. You can hit M on the keyboard to toggle mute off. Then you can adjust the volumes up.
To test whether sound is happening you can run:
or play a sound file, e.g. a .wav file, that you select from somewhere under the /usr/share/sounds directory or download a test sound file from online. The speaker-test outputs white noise, so you may prefer something more listenable.