I’ve experienced the “missing HDMI” option when my TV is turned off (or perhaps on the wrong input??) while the Recalbox is booting. Not sure on the exact timing but it’s definitely fixable 100% of the time if the TV is turned on first.
I didn’t used to have this issue before 8.x series Recalbox so not sure what may have changed in I guess the RPi firmware or perhaps the Linux kernel side. I suspect the hdmi_forceplug or one of those boot options will fix the issue but I no longer use HDMI so can’t test.
Heck, you could even use a boot option to lock-in HDMI as the only audio choice if you don’t care about easy access to the audio jack functionality!