This is a great question! Thanks for asking!
The amount of writing really depends on your major. Some majors -- like history, political science, or journalism -- are really writing-intensive. The courses in these majors may require many essays in a single semester, perhaps up to 10-15 pages of writing outside of class. For example, see the University of Washington's advice: https://www.washington.edu/uaa/advising/degree-overview/general-education/additional-writing/
Other majors -- like engineering or computer science -- don't often see a lot of essay-writing in their curriculum. I was an engineering professor for eight years and I only assigned a handful of two-page essays. Instead, the kinds of writing that we do in that major are writing software requirements or specifications or writing working code.
Different majors require different kinds of writing. But, the better the communicator you are, the more successful you will be in your work.