No voltage detected at black wire, voltage detected only at red wire coming from ceiling outlet
In the US there is no standard specified if the red or black is the hot for a ceiling fixture fed from the switch location.
I usually do use black for a light ,and the red for a fan but I have reversed it this in the past.
Both the red and black can be hot and or switched fixtures.
If the power was at the ceiling it is now common to take the black down as hot and the red is a switched hot but not all electricians do this because there is no code requirement to do it.
So if the red is hot with the switch on and not hot with the switch off cap the black and connect to the red,,, electrons don’t care what color the insulation in and the NEC has no requirement in this case for the red or black but black is more common so the mfg showed that.