How should I redesign my assessments in light of widespread AI use among students?

This is difficult to respond to without more context about your discipline, intended learning outcomes, setting of the class, etc.

Generally, it might be good to consider what it really is that you want your students to be able to do at the end of the course, both by themselves and possible with AI support. How would you be able to see that they can do it?

If you see it best in a long text and writing in itself is really important to you, maybe you can scaffold the writing process and ask students to write an outline or abstract in class, discuss it with them (possibly in several iterations over several sessions), and then ask them to finish it at home. That way you are part of the writing process and see things develop in real time.

If writing itself isn't an intended learning outcome, maybe the essay can be replaced by some other form of assessment. Possibly oral, like an examination, presentation, group discussion (be careful to design those in an inclusive way so students with test anxiety or difficulties to express themselves spontaneously in the language of instruction aren't disadvantaged). Possibly in some other product like a short video or a poster that they then defend. Maybe they can collect in-class works in a portfolio to which they add reflections of what they learned from each piece and why that matters in relation to the course's intended learning outcomes.

One suggestion would be to talk with your students, or possibly students that took your class in previous years, and ask them for suggestions of how they would like to show to you that they have learned what you wanted them to learn. They might have great ideas!