Agreeing with other comments here, it is relatively normal to have only 2-4 hours of measurable or direct productivity in an 8 hour workday. You write that you

Agreeing with other comments here, it is relatively normal to have only 2-4 hours of measurable or direct productivity in an 8 hour workday. You write that you 'only' seem to be able to do 2-3 hours of work before needing a large break. That is quite impressive! Furthermore, a large break is likely warranted at that point. Perhaps you could experiment with taking breaks more frequently? Also, do not underestimate the value of doing something unrelated to stimulate your problem-solving ability...