It seems to be implied that for either category, any%/True Ending, you need to start a New journey. Is that true or can we start a ng+ run and complete the category as we like?

Community is considering adding NG+ cats, but needs time to decide specific rules.

Yes, the current rule is to open a new archive. The NG+rule has not been added yet, so you need to open a new archive in the category you are currently participating in