There must be multiple sources of this issue, and different variants of it. Apparently sometimes it's high memory usage, sometimes it's Intel audio processes (if somebody in one of the Apple Discussions was right).
In my case, I finally found the root cause: the PiPifier Safari extension. I have no idea how or why it would cause the popping, as it did it even when the extension wasn't actively in use and I was watching full-screen video. But I'm 99.9999999% that was it, as I had constant pops before and now that it's uninstalled I've had zero over the past five days.
I also deleted the .plist files and rebooted after uninstalling the extension, but removing the files alone and rebooting had only temporarily (for ~one hour) solved the issue previously. For reference, I'm using a 14" M1 Pro MBP. I wasn't getting the prolonged low-pitch grumbles that some people were getting, but rather intermittent high pitched pops. All gone now! So happy.