LG Display via USBC-HDMI indicating as active even after turning it off I have an LG 4K display connected via USBC-HDMI cable.
After turning it off physically with the button it remains active in MacBook Pro 16 settings and I can move the mouse there.
It happens also when connected via Apple adapter + HDMI-HDMI cable.
And it's working fine when connected via USBC-DP cable. When turning off the display, Mac switching to the internal display only mode.
The USB-C ports on most MacBook Pro laptops all natively output a DisplayPort signal.  Most are Thunderbolt 3 though there are a few that are only USB with Alternate Mode display.    So, when you go from that USB-C port to HDMI, you're converting the signals.  That signal may stay high because the conversion isn't &quot;clean.&quot;  This is why I always recommend using an active adapter that will recreate the signal versus a passive one that just &quot;rearranges the signals.&quot;   I believe that will sort your issue as well.
However, on a DisplayPort input on a monitor, there's no conversion - the signal is clean.  So, when you turn it off, it's off.  If you can use DisplayPort, then I recommend that over HDMI There's no conversion and it's a better signal.
What you're seeing is just one of the many idiosyncrasies of HDMI.  If you're going from a HDMI source to an HDMI end device (monitor/TV), it works fairly well.  However, the moment you have to convert, that's where things start to go sideways.

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