The Canvas syllabus can be retrieved from the courses API endpoints. It is one of the optional include parameters("syllabus_body")
You can include it in a users list of courses:
Courses - Canvas LMS REST API Documentation: List courses for a user
Or if you are getting a single specific course:
Courses - Canvas LMS REST API Documentation: Get a single course
You can also update the syllabus information via the courses API:
Courses - Canvas LMS REST API Documentation: Update a course
To get the syllabus for each course in an account, you can use the accounts API This has the same include parameter as the specific courses, but will return a paginated list of all course in an account.
Accounts - Canvas LMS REST API Documentation: List active courses in an account
Depending on how your institution and sub-account structure is setup, this could be a very large number of courses. You will have to use you best judgement on if it is more efficient to get all of the courses in an account or use multiple calls on the courses endpoints to just get the courses you want.