CE is in the ECE department at Ohio State and students follow either an EE or CE pathway. It’s a direct admit major. CS/CSE is a separate department.
https://engineering.osu.edu/undergraduate/future-students/admissions/new-students
The National Buckeye and Maximus scholarships (apply by Nov 1, EA for best consideration) also stack with ECE department and CoE scholarships (application through Ohio State’s scholarship universe opens in Dec.) so being in the $40k ballpark is very possible even with the $4,000/yr engineering fee.
Applying by Nov 1 (that means you’ve submitted your application and documents) is important to avoid getting bumped to RD. Apply soon and continue to followup until you verify everything is in.