I suspect it is because it is a chromebook that there might not be a linux kernel driver for it.
Please open a Terminal (just type terminal in menu search bar and press enter key) then copy and paste the following command clicking on the 'copy to clipboard icon at the end of the comnand, then in terminal right-click and select 'paste', then press the enter key. You will be asked for your password to elevate you to root.
Then run sudo update-grub and reboot. The parameter snd-intel-dspcfg.dsp_driver=2 forces the kernel to load the SOF driver (sof-audio-pci-intel-icl ) instead of the legacy snd_hda_intel .
Ensure firmware is installed : Install the latest sof-bin package (e.g., sof-bin-2024.06.tar.gz ) and place firmware files in /lib/firmware/intel/sof/ .
Editing GRUB: yes, I tried. But no sound. I tried to change from snd-intel-dspcfg.dsp_driver=2
to snd-intel-dspcfg.dsp_driver=0
and got several hardware output devices. But no sound.
Well if your bluetooth headset also has microphone capability then no, it doesn't make sense. It is down to what your preference is. Hopefully there might be another forum member who has a similar setup to yours that can advise.
I try to help where I can friend. I'm in the middle of rewriting the Unofficial Manual for Zorin 18 Core as I have discovered major flaws in ones I uploaded at end of last year. Additionally there have been some bug fixes with the release of Zorin 18 r3, so the one I am working on will be more up-to-date. Even the installer picture is a big improvement.