Does adding the full pack make the wine really sweet?
You don't need to add the entire pack -- bench test and add only as much as you want.
However, based upon the feedback from others, the wine is acidic and needs the sugar to balance the acid. I have a few bottles of a NY Vignoles that is rated "sweet". While I can taste sugar, it tastes off-dry, as the wine is highly acidic.
I also have FWK Blackberry and Strawberry in production. Both kits came with 2 backsweetening packs, and I added 1 pack to each before bulk aging. The wines did not taste sweet at that time, and actually had a bit of a bite. Take that with the understanding that the wines were very young. Others who have made the kits have put the full 2 pack in, and while I'm a dry red drinker by preference, I am currently expecting to put both packs in each wine. I'll bench test but expect the acid will require all the sugar.
Because the syrup is so thick, you have to stir REALLY, REALLY well to get it to distribute. I use a drill-mounted stirring rod, get the wine moving, and have my son slowly add the syrup in a fine stream. After the addition, I change direction and stir for a minute. Then taste. When you get to the point you think the wine needs just a bit more