Just confirmed, 11th Gen manufactured after August 2021 to 13th Gen all used Tempo.
If you want to use the audio jack over USB or Bluetooth/wireless, the the audio expansion card would be the best bet.
Now, it is likely possible to try and fight with it by tweaking allowed rates, default rate, etc. But I’d need more information on which distro and release.
On Fedora for example, we could try disabling power saving. Will it help? Probably not, but it’s worth a try. Just changes a 1 to a 0.
sudo echo 0 | sudo tee /sys/module/snd_hda_intel/parameters/power_save
If this worked, you can make this survive reboot:
echo "options snd_hda_intel power_save=0" | sudo tee /etc/modprobe.d/snd_hda_intel.conf
But this again, may not help.