When you read many genuine posts from the same poster, you develop a keen recognition of their writing style, thought process, vocabulary, speaking style, character depth, and mental acuity.
When these things suddenly change in this day and age, there is but one answer - and it is not night school.
You have a much harder job since you are not afforded that luxury. But I can tell you what I would do (it was something that an ND professor did for my writing class way back in the day for different reasons…….
….sit them in your class and have them write with you watching them as they are asked to write their essay in an hour or two. Also, do not tell them what the essay will be about - just that it will incorporate the topics and principles that you covered (otherwise they will just use GPT ahead of time).
I realize that some of your students (if not most will not feel comfortable with a pencil and a Blue Book), but even with laptops, you can roam and get a view of what is on their screen. You can also have them verifiably disconnect from the internet as well.
The essays won’t be as good, but everyone will be under the same restrictions so it will be fair.
It’s really your only option as AI will get so good that those programs profs used in the past to catch AI will be outfoxed (I assume they are already being outfoxed).