You need to look at the situation before the change and the situation after the change to make any conclusions.

Before the change, anyone with symptoms could be tested in Sweden, although all slots were at times fully booked. I don't know if people with more serious symptoms were more likely to book a test (thus increasing the positivity rate) or if the probability to book a test was uncorrelated to the seriousness of the symptoms.

After the change, only people working in certain sectors (such as health care and elderly care) are tested if they have symptoms, others are not tested unless hospitalised. I suspect that health care and elderly care workers with very mild symptoms are more likely than others to take a test as they are more likely to be concerned about the risk of infecting others. This would suggest that the test positivity rate goes down if the infection rate is constant. On the other hand, those who are hospitalised are much more likely to be infected although some could be hospitalised for other reasons. This would suggest that the test positivity rate goes up if the infection rate is constant.

With one factor increasing the test positivity rate and one factor decreasing the rate, it is not clear which one would be dominant, so I don't think that you can make any conclusions from the positivity rate about the infection rate. I think it's better to look at the hospitalisation and death numbers as those are harder to hide in the statistics.

I don't know how testing has changed in the rest of Scandinavia.