I have no sound output through HDMI on 5.10.73-1 or 5.14 or 5.15

This has been discussed in the pi kernel thread. Starting with the 5.14 upstream they made a lot of changes and over time code changes has affected the current 5.10. The sound has to be configured differently in /boot/cmdline.txt depending on if you are using kms or fkms. In the tail end of cmdline.txt is where the change needs to be made with these newer kernels with :
snd-bcm2835.enable_compat_alsa=
If you want headphones also add:
snd_bcm2835.enable_headphones=1

fkms: (Note the number in bold)

mousepoll=8 snd-bcm2835.enable_compat_alsa=1 snd_bcm2835.enable_headphones=1 audit=0

kms: (Note the number in bold)

mousepoll=8 snd-bcm2835.enable_compat_alsa=0 snd_bcm2835.enable_headphones=1 audit=0

Sometimes if not set right you can also get a black screen before the Greeter.

A couple more thoughts. If snd-bcm2835.enable_compat_alsa=some-value it will boot with headphones only depending on if it is kms or fkms. And last I have found that switching back and forth testing sometimes when it is booted up it defaults to headphones and I have to switch to to hdmi.

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