Here is my experience with both a EF9500 and OLED65E7 with DTV 4K on the C61K
First you need to make sure "HDMI ULTRA HD Deep Color" is enabled on the C61K HDMI port (General Menu)
Second all broadcasts are shown as HDR HLG, the HDR flag in the guide just means that the content was originally recorded with or in HDR.
Third the OLED65E6P and all LG's OLED's work with HLG, just make sure to have the latest firmware as noted.
Forth and last - make sure your HR54 is on the latest firmware or close, HLG was enabled I think in FFC and later but I can't remember. I don't believe it will work if you have an early version of the new GUI and for sure not the old.
Note HDR / HLG is dark on the EF9500 but that's what I get for buying early in.
Note avoid the AVR until you have things working (go direct to TV from the mini)