How much time do you actually need at the Anthropology Museum in Mexico City?

I'd allow around three hours on a short trip.

You could easily spend most of the day there, but the museum is huge and trying to see every gallery gets exhausting.

I'd prioritize the civilizations you're most interested in, especially the Mexica, Maya, Teotihuacan and Olmec sections. Visiting before your Teotihuacán trip also gives you much more context for what you'll see there.