Utilising assignment for thesis
I'm still not sure that I understand the entire scenario, so this will be a bit hypothetical.
If you write something but it isn't published in any form then, later, you can simply copy and publish any part of it without citation or further comment. It isn't self plagiarism to use your own unpublished work.
Assignments in a course might, however, follow some rules beyond those generally accepted in scholarship. If the thesis is at the same institution as the earlier coursework, then, for purposes of keeping the faculty happy, it would probably be wise to mention that some of what you write was written earlier for a course.
But normally, student work for course assignments isn't really published, though it is shared in a limited way (with the professor). There can be exceptions, of course.
A way to be safe with all sorts of plagiarism, including self plagiarism is to cite if there is any doubt at all. Over citation will not, generally, be a problem. Under citation can be.