The big problem with all ChromeBooks is they are all different.
The only time they seem to be in any way the same, is if they are using the exact same motherboard and CPU setup.
But that is not even 100% correct, from different manufactures of the ChromeBooks.
Yours is just one of the ones that sound is a real issue, to get working.
On my HP 14 ChromeBook
BookwormPup64 10.0.7 is the first Puppy Linux version, that had working sound, the first time I booted it.
All other Puppy Linux versions, needed some type of tweaking, and most needed the Linux kernel replaced.
ozsouth (the Puppy kernel expert) actually compiled a special kernel for ChromeBooks, to use with Puppy Linux.
Basically, he took and configured it, with a lot of the stuff activated, for support of ChromeBooks.
But not sure, it is good to use in newest versions of Puppy or even if, it would fix your issues, with Apolo Lake sound issues.
The Linux kernel, has hundreds of config settings, that can be setup, when it is compiled.
More and more settings are being provided, specifically for ChromeBooks, in newer and newer kernel versions.
The people controlling what is in the kernel, seem to be embracing the idea, that Linux is good to use on ChromeBooks.
So, trying to get the kernel to support them more.
Basically, the kernel is what provides the drivers and firmware to run, control, and use the hardware.
your issue seems to be about the needed firmware and config settings, in the Linux kernel.
the last idea I offered is doing exactly that.
Changing the firmware software file and putting commands in modprobe.d, to change/activate kernel config settings.
We offered you the way to change the kernel in BookwormPup64, earlier in this topic.
You want to try it??
Note:
What is done to some other Linux operating system, is usually never going to work exactly, in a Puppy Linux version.
About all Puppy has in common, is using the same core Linux files and programs, that all Linux OS's have to use, to be Linux.
The newest Puppy versions are trying to have a common Linux file system layout.
But Puppy even has a few things different in it.