How to write a research proposal for a PhD position where the description of the project is given?
If the research project description is very specific, think of it as a job application.

The research project is the job advert.

The research proposal you will write up and send out is your cover letter. You ought to demonstrate how you're the best fit for the research project.

Approaching the research supervisor in advance of the application deadline would be good, if their details are given as part of the project description.

One cannot assume that 'the supervisor knows how they want to complete the project'. One supervisor might be very prescriptive, the next supervisor will be very open-minded or loose.