3 updates (including today's) later and the error about hdmi-audio-codec is still there. I even removed the third party binary addon that I had, but nothing changed.
When it just happens at boot, e.g. now that it happened "only" 6 times, right before the system finishes its boot process, things are generally fine and I can connect via ssh and do stuff.
When it happens after all that, it fills dmesg and I must stop kodi so as to do anything because the lag is very annoying and the green led does not stop blinking! Earlier, it even disconnected me 10 seconds after stopping it and returning to the prompt!
I will keep updating it daily until Sunday. If the forementioned issue is still there, I will probably leave it aside and update it weekly or biweekly, just to be on track until the next alpha of kodi.