So as you are starting with Cursor i highly recommend going through the Docu to learn what it can do… and how to use each part
Yes it would help to ask it to split parts, depends on what language you use (looks like JS?), AI can then use import statements to include those separate files into your ‘start file’.
Usually its a good idea to do modular programming (split functionality into modules or classes or functions, depending on language or framework).
If you tell AI to use for example Single Responsibility Principle as guideline when coding it will not mix different features in one file. You may also create rules (see docs) that tell the AI for example to keep files under 500 lines limit (a bit over is not tragic but the more lines the harder it will be for AI)…