Tl:dr we have priority at hundreds of intersections but it doesn't work very well, either due to near side stops (downtown) or long red times (ROWs).
Nearly all signals on the streetcar network allow streetcars to extend the light by up to 30 seconds, typically also with a Walk display but sometimes including up to 16 of don't walk (this allows the signal to respond much faster and reduces unnecessary extensions). The problem is that nearly all signals also have nearside streetcar stops which means that the estimated time that the streetcar would like to enter the intersection is usually wrong due to dwell time variability. It the streetcar dwells longer than expected, it may miss the end of the 30 s extension, in which it needs to sit through the entire red - meanwhile if the light hadn't extended the green, that red would already be nearly over by then. If the streetcar takes less time than expected, the system may choose not to extend (to avoid the situation described above) when in fact the streetcar could have made it through within a 30 sec extension.
The issues on ROWs (which usually have far side stops) are different. In that case part of the issue is that there are very long cross street green times due to pedestrian crossing distances, and left turn phases. The solution in those cases is to permit streetcars to insert a short green between the cross street phases and the left turn phases. The system is perfectly capable of doing this, but as far as I'm aware there are only two intersections where transportation services has approved inserted phases to reduce delay for streetcars going straight.