How do you actually complete a scenario in Planet Coaster
Click the second thumbnail.
The three blocks in the left column of the panel to the right indicate the three levels that are part of the set of levels called "Captain Lockjaw's Buried Treasures". The blue background indicates you currently have the 1st block, associated with the first level, selected.
If you look closely, these track your progress within the set. The three icons below the teaser thumbnail for the level indicate the currently best achieved star rating for the scenario. In your example you fully completed the first level.
A level is counted as complete typically after getting at least one star. When this happens, the next level is unlocked. You can see that it is due to a subtle difference: Unlocked levels use color thumbnails, while locked levels use grey thumbnails. Click on the second thumbnail to play the second level in the set.
It appears the UI shows a lot of information in its iconography! Also see this little diagram if my descriptions are unclear to you:
Sidenote: This also clears up the meaning of '3 ouf of 9'. There are three levels in the set with three stars each. Thus there are 3x3 = 9 stars in the whole set. So this bit of text tracks the progress of achieving goals for the whole set.
You have completed the "Pirate Battle" scenario. The game allows you to continue playing, in case you are having a lot of fun with that particular park or you want to finish something you were working on. However, there are no more stars to get on that map. You should have seen a popup when you obtained each star. The popup for the third star serves as a "level completed" screen.
The reason "Captain Lockjaw's Buried Treasures" shows you having 3/9 stars is because it contains 3 scenarios. You have all three stars from "Pirate Battle", but there are two more maps with 3 stars each, which you haven't earned. These maps can be accessed by clicking the vertical tabs to the left of the scenario description in your screenshot.