I was surprised the Northern Canberra tram didnt go to Bruce Stadium too
The first stage doesn't go anywhere near Bruce (black line on the map below).
Stage 3 (IIRC) will be the line that goes to Belconnen, through Bruce. Current plans have the line going up Haydon Drive around the front of Calvary hospital, which is within easy walking distance of the stadium.
However there are plans for an alternate route where the line would go around the back of the hospital and directly past the stadium, and there's still support for it to go that way, but the argument against it is that GIO and the AIS Arena are going to be replaced so you don't need the line to take the longer route past the AIS.
The blue line is the planned route, the red line is the alternate that would go directly past the stadium.