You have to have a permanent resident permit and to have stayed for 5 years. Unfortunately I can't find anywhere on the Swedish immigration site (in English anyway) that lays out the requirements to receive said permit.

The 'ton of money' comment were for people who wish to use pathways open to people who bring large investments into the country.

Depends on the route you took (work permit/studying/joining a family member), but if you are on work permit (and are a non-EU citizen), you can get it after 4 years of being on a work permit. (These 4 years count as part of the 5 for citizenship, so it's 4 for permanent resident + 1 more.)

https://www.migrationsverket.se/English/Private-individuals/... (Ctrl+f "Perma­nent resi­dence permit")

Yep, significantly cheaper to become a citizen in most (if not all) EU countries than to renounce US citizenship.