[Leopold]

Thanks, the post by popcornmix on that thread was probably what I was thinking of. When I turn off the TV it also sends a shutdown signal to the Pi so that's not going to work for me. I am unable to configure this behaviour as I have nothing showing in peripherals.

What do you mean by "nothing showing in peripherals"? No libcec entry at all or not a setting to prevent the RPi from shutting down?
With just "hdmi_ignore_cec_init=1" as the only CEC related setting in "config.txt" I do have a libcec entry in the peripherals section, so should you.
Do you happen to have any other CEC related settings in "config.txt"? That might prevent the entry from being added.

I tried again and the cec adapter was shown, so that must have been a temporary glitch. I disabled the option that shuts down kodi when the TV is turned off, and now power toggling the TV does fix the media buttons. I'm not sure yet if this is a better solution than hdmi_ignore_cec_init=1 but it's good to know there is another way of working around it. It would be great if a proper fix could be found. When I get a chance I'll try cec_osd_name=kodi.