SQL Server doesn’t track the number of changes to the database is a counter you can grab. The best way to figure this out is to work with the application developer and see how many database calls there are, and how many of those are read and how many of those are writes. Then work with the business to see how many times each of those calls would be used per person per day.
The easiest way to see read to write percentages would be to look at the IO load. Monitor the read and write requests to the disk. It won’t be a perfect number as not all reads will go to the disk, but it’ll give you a ruff idea.