Fixed it.
Setting up a Construct project
To use TypeScript with a Construct project, you must first save the project as a folder. This means it's made up of individual files in a folder, rather than everything being contained within a single .c3p file.
To do this, choose Menu ► Project ► Save as ► Save as project folder... and choose a folder to save the project to. If you're starting from scratch, you can also create a new project and then save it to a folder.