It sounds like the yeast in the Sarsaparilla kit might not have been active enough, especially since you’ve had success with other brews like ginger beer and Canadian blonde. If the Sarsaparilla is already brewed and sitting in the fridge without much alcohol development, adding fresh yeast could work, but there are a few things to consider.
Firstly, Sarsaparilla kits tend to have a lower amount of fermentable sugars, so there may not be much for the yeast to consume. Adding more sugar (such as a bit more raw sugar or honey) could give the yeast something to feed on, but you’d also need to ensure that the yeast you pitch is healthy and active. I'd recommend using a yeast nutrient as well, to give the new yeast a boost.
Bringing it out of the fridge, warming it up, and pitching fresh yeast could get things going again, but it’s a bit of a gamble. If there's not enough fermentable material left, you might not get the result you're hoping for. You could risk introducing off-flavors or over-carbonation if fermentation suddenly kicks in too hard in the keg.
Maybe try a small experiment: take a small sample and add a bit of sugar and fresh yeast to it, and see if it starts fermenting actively. If it does, then you could consider scaling that up in the keg. Otherwise, it might be best to just enjoy the Sarsaparilla as it is, even if it’s lower in alcohol than expected.