As far as I'm aware, there isn't a good way to see this. The only way I'm (somewhat) aware of is to mouse-over the district after it's been completed. The value is the total of all it's yields, not just the adjacency bonuses, though. So, if you have 6 envoys at 3 commerce CSs, all your commerce zones will have +6 gold, in addition to their adjacency bonuses and any other modifiers like social policies.
Showing how the new district affects other districts would be useful not just for yields, but for appeal as well. Dropping appeal has obvious effects considering neighborhoods but it could also affect the placement (or non-placement) of a national park. Furthermore -- what happens if your place a national park, then build an industrial zone next to it and when of the tiles drops below "charming" appeal?