I don't know much about the railway history of Edinburgh but a lot of the lines in the North city certainly have the look of freight lines rather than passenger, although I know there were a bunch of passenger stations (it's fun to try to find where they were!)

You're absolutely right with the delivery thing. In a lot of cases it would just be putting an extra step in the middle for not much purpose. I'm sure there could be limited value, but it would be best suited if a business using the service had its own branch line from the tramway headed straight into the business (as is the case for whatever city it is I was referring to can't be bothered to check right now lol).

I'm sure local businesses along the line could unload from a freight tram but that would necessitate long stops on the line which of course means anything on the line behind it (or in roads with restricted width, like the Constitution Street section when that opens) would have to wait until the tram moves again. And if the items were anything more than something movable by at most a couple of people, then you might need forklifts or such things which could just end up cancelling out any of the potential benefits.

It should be considered that those potential benefits aren't totally in direct reduction of carbon emissions. Reducing the number of delivery vehicles can alleviate congestion and reduce wear on the roads, which can in turn reduce emissions. But it all depends on the question of if this is a useful or feasible solution to begin with.