Ok, just tested the trade route yield,
-There is no relation between district adjacency bonus and trade yield.
-There is no effect from population, at least not from population from 1 to 11 pop
-There is no effect from era/tech, at least not from ancient to renaissance
But some districts give more than others:
City Center: 1 food, 1 production
Campus: 1 food
Encampment: 1 production
Commercial: 1 production
Theater: 2 food
Industrial: 2 production
Holy Site: 2 food
Harbor: 2 production
Entertainment: 2 food
Also, if you increase the trade route yield when the trader is still walking, you start to get the upgraded value.
TL;DR yet another reason why campus district sucks in Civ 6.