Hello, sorry for late response. I don't think we can help with hardware support issues. We're a small team and we really focus on bugs specific to Kali.

If support for your sound card is missing in the kernel, all you can do is wait for a newer kernel. You can also try to install the package firmware-sof-signed, it contains firmware needed for some sound cards. I don't know if it will fix your issue, but it doesn't hurt to try.

Otherwise... more google searches :) If your sound card is unsupported, you're not the only one impacted, you should find some information out there.

Finally, I looked at your ALSA report log (thanks for providing it). There's no obvious error that stands out to me, but I'm really not a specialist in linux audio...

So, in short, sorry we can't help. I'm closing the ticket since there's nothing we can do.