The change in testing should eliminate false positives, so it should have little to do with hospitalizations.
Testing positive has had little to do with actual number of people getting hospitalized. The PERCENTAGE OF THE POPULATION that ends up in the hospital will probably remain the same, or perhaps decrease as those more likely to die are removed from the population and herd immunity takes affect. The percentage of those tested that get hospitalized is actually likely to go up as the test are allowed to become more accurate. Of course the covid variants might influence this.