With the caveat that drug offenses include manufacturing, trafficking, and sales:
Your data is consistent with my claim: I meant the denominator being the prison population, not the entire population. Sweden has about 8600 people in prison so about 37% of their prison population is in there for "drug offenses", whereas in the United States it's less than 1 in 5 per your Prison Policy citation. Obviously if you treat entire population as the denominator, then any comparison of Swedish and American prisons is useless because we incarcerate a much larger percent of the population.
Edit: I realize my original comment said "people" not "proportion of people", but in my defense interpreting it to be people literally is a bit absurd. Sweden's population is about 30x smaller than the United States, so there's no way the counts are comparable!
Edit 2: Actually no I did say “As a percentage”. Whew.
Next, you can see from this sample of federal prison (table on page 2): though drug offenses were the most serious charge for half of prisoners, only 0.1% was for possession. The rest was for trafficking and sales. https://bjs.ojp.gov/content/pub/pdf/dofp12.pdf
This data is from 2010, and the United States has undergone a decriminalization revolution since regarding possession, so new prosecutions are even less likely to be possession claims.