Quick rule: when the exposure and the outcome are both counted for a whole group and never matched person to person, the design is ecological.
Here cigarette sales (the exposure) come from a tax department total, and COPD numbers (the outcome) come from pooled hospital records. No single person is recorded as both a smoker and a COPD case, so the correlation is drawn at population level. That is the defining feature of an ecological correlation study.
Eliminate the rest fast: a cross-sectional study needs both exposure and disease measured in the same individuals at one time point. Operations research studies the working of a programme to fix bottlenecks. A posological study is about dose. Since only aggregate population figures are compared, ecological study is the fit.
Watch the trap of ecological fallacy: a group-level link does not prove the same link holds in individuals. Ref: Park PSM, 24e.