The highway in question has been a weird-ass pet project since the 60's. It's been routinely denied and shelved many times, but after Stockholm implemented congestion tolls in 2006, it had a resurgence.
Originally it was all aboveground and bridges, but the reason it's now morphed into the longest road tunnel project in Sweden, is because the response to every small NIMBY protest has been "fine, we'll dig it down, but it'll cost more". Note that it's still aboveground in some places, and in something that I'm sure is pure coincidence, those areas are among the least affluent residential areas of Stockholm. Note that everyone living above the tunnels will still get to enjoy years of underground rock blasting, I'm sure that'll be fun.
And since almost the entire highway is now in a tunnel, and since it's going to be the longest in Sweden, the budget has gone up dramatically. How to finance it? Oh, our glorious politicians decided to use money from the congestion tolls. Never fucking mind that the initial promise of those were that the funds were going to be used solely for public transportation projects and improvements - things that would actually solve congestion. But all of that is now put on hold for the next 10-20 years, because this one road eats all the budget.
Yet another criticism is that the highway doesn't really solve the problem, because there's actually very little existing traffic that goes between the points it will connect. Truck transports from the south of Sweden to north of Stockholm take different routes already, they don't go through Stockholm. So you won't get rid of all the heavy traffic that's currently congesting the E4, because most of that is actually going into or out of Stockholm. All the ports of Stockholm are over on the east side of the city. Yes, if you live in the far west suburbs of Stockholm, you now get an easy way of going to the southern suburbs, good for you, but that's going to increase total traffic, not decrease it.
But the most annoying thing about the project is that in this latest round where a ton of challenges forced it underground into tunnels, which resulted in significant increases in cost and time, noone has re-evaluated what the traffic situation in Stockholm is going to be like in 2026 when it's estimated to be completed. (Note: Of course it won't be completed in time or on budget, so 2026 is highly optimistic already). Here on Hacker News there's regularly articles about our glorious new electrically powered autonomous rideshare future of transportation, but this highway project doesn't take any of that into consideration. They're just assuming that traffic will increase like it has the past few decades, they're assuming it's going to be 100% ICE-powered human-driven cars. And yet you have articles like this which heaps praise on the environmental concerns and solutions of yet another ridiculously expensive highway that noone really needs or wants.