Student needing encouragement (?) to write

I am an instructor for a short summer writing & reading class with four students. The students are great with participation and the analysis activities we do, but the actual writing part of the class is not their favorite. Despite this, three out of the four students do their best to complete the in class essay or paragraph responses I assign them. One student, I have noticed, is really lagging behind in these longer writing activities. They will generally write a sentence or two then draw on their paper or just sit there during an essay assignment.

I have repeatedly made sure that all the students understand the essay prompt and expectations for their response. I even do activities with them prior to this long writing activity (like finding direct quotes from the text we read that given day and what it reveals or possible commentary) that they can refer to help them in their essay. I have also tried breaking up these essay assignments into smaller paragraphs/ provide tips for mind maps in case this student feels intimidated by the assignment. This student is not struggling in any other activities and has shown they can thoughtfully respond to the prompt verbally, but they just completely disengage for written activities.

This student has said before that they do not like writing or reading, so that may explain a bit (parents likely signed them up for the this class to refresh skills for the upcoming school year).

I am unaware if the student has ADHD or any learning disabilities that would impact their performance. If they did, I feel like the program director would have told me so I could prepare for differentiation accordingly.

I have tried just about everything but sitting next to the student and holding their hand through the essay. Any tips on how to encourage the student? I really want them to succeed and get something out of the class, but I fear if they do not complete these assignments I cannot help them much.