Done all that, function 10 just shows me the HDMI and "the other thing I forgot the name of".
Another thing, when I check either one of these options (Auto, HDMI and "Phono?) I got an error message...(sorry for not being more explicit).
Same power supply for either the Pi3 and Pi4 I always used.
Will this HAT show up under "advanced - audio menu" in normal conditions without any tampering from us users?
If so, it's a FUD.
Yes.
And option 10 should show this (I have one):
Card 0, ID `ALSA', name `bcm2835 ALSA'
Device 0, ID `bcm2835 ALSA', name `bcm2835 ALSA', 7 subdevices (7 available)
1..2 channels, sampling rates 8000, 11025, 16000, 22050, 32000, 44100, 48000, 88200, 96000, 176400, 192000 Hz
Sample formats: U8, S16_LE
Device 1, ID `bcm2835 ALSA', name `bcm2835 IEC958/HDMI', 1 subdevices (1 available)
2 channels, sampling rates 44100, 48000, 88200, 96000, 176400, 192000 Hz
Sample formats: S16_LE
Card 1, ID `sndrpihifiberry', name `snd_rpi_hifiberry_dacplus'
Device 0, ID `HiFiBerry DAC+ HiFi pcm512x-hifi-0', name `', 1 subdevices (1 available)
2 channels, sampling rates 8000, 11025, 16000, 22050, 32000, 44100, 48000, 88200, 96000, 176400, 192000, 384000 Hz
Sample formats: S16_LE, S24_LE, S32_LE
Maybe it took a EMF hit from lightening?
If you have a different Pi, try the HAT on it to see if perhaps interface circuitry on the Pi it's on is foobar?