Is a longitudinal study really by definition/always correlational?
How about a repeated-measures experiment: I would've called that an experimental longitudinal design. (For example, you randomly assign subjects to 1 of 2 groups; you collect data 1x before a manipulation, 1x right afterwards, then again 1x in a 3-year-follow-up.) ... or is that a contradiction in terms?!
How about this even more specific scenario:
week 1: Group A gets a drug, Group B a placebo
week 2: neither group gets anything
week 3: Group A gets the placebo, Group B the drug
data collection at the end of each week.
Now, does it matter how you analyze this/ which research question you ask in order to "define" the design? e.g., if you just use a t-test of week 3 data, you've obviously neglected all longitudinal aspects and would call it an experiment... but would it work the other way around, so when you are mainly interested in the repeated measures-aspect, that you could call this longitudinal, but still enter all data into your analysis (e.g., an ANOVA, or even better, a regression analysis?