Except they are now rising again rapidly in Stockholm for instance [1]. You can use the html console to remove the overlay to read the article. They also were never on "almost no cases", they have been higher than the neighbours all the time except for a very brief period where they were on the same level.
They are not. Cases are up slightly in the past few weeks, but on par with where they were in July (after
which they saw a decline). You have to be extrapolating wildly to call this a rapid increase.
Sweden started July with a bit more than double their current cases, and ended it with a bit less than half. Four weeks ago was as low as it ever got in Sweden, and since then it has risen steadily, up to more than double what it was. It's also 30% higher than the last local maximum, in the middle of August.
That's not unreasonable, though you referred to cases and not deaths in your original post. Deaths lag a couple of weeks behind cases, so maybe the local minimum in deaths in Sweden corresponds to the local minimum in cases 4 weeks ago. But maybe not!
[1] https://www.dn.se/sthlm/antalet-coronafall-har-fordubblats-i...