That is true -- but most of that traffic is traveling to or from destinations along the route, such as central Stockholm, the ports, or some of the nearer suburbs. Quite few vehicles actually go from Huddinge (or south) to Kista (or north).
This huge project is a "bypass" and it'll work as any other bypass in other cities around the world. Which means any kind of traffic moving from North to South and vice versa, will bypass entire Stockholm, and right now I see huge amount of traffic every day on this route.
I don't remember the exact numbers, but out of the heavy truck transports currently clogging up Essingeleden, only 2% (Or was it 0.2?) or less would actually benefit from Förbifarten, because there is very little existing truck traffic going from way south to way north of the city.
> right now I see huge amount of traffic every day on this route.
Yes, but most of that is going to places along that route. So you won't move a meaningful amount of existing traffic, you'll just enable new traffic. That's generally good, growing regions need more infrastructure, but my point is that Förbifarten is the wrong way to spend that money. It's a prestige project at this point.
If you had to spend that money on roads, I would have much rather seen Österleden, because completing the highway ring around Stockholm actually makes sense, there is plenty of traffic from the ports to south of the city, and by making the full ring, that traffic would get a choice of direction around the city depending on time of day and commuting patterns. And this holds true for every trip across opposite ends of the city.