There is a huge spike in active cases right before and after Dec 11th. More cases = more deaths.
Present day we have about 430k active cases, which is almost 10% of the population, but the % is still 2.3%.
Vaccination has continued in Denmark so if vaccines were killing people we'd expect to see that rocketing as Denmark has one of the highest vaccination rates.
I think the causality is:
More illness -> More people get tested
More illness -> More people get vaccinated
More illness -> More people die
The reason we are testing 200k/day is because you don't have many options for moving around without a valid test or vaccine. Ie. school, shopping, work etc requires it.