For most of us--myself included--once you graduate from college, the answer is: "enough to not get fired". This is far less than most curriculums ask you to know, and every year, "enough to not get fired" is a lower and lower bar. With LLMs, it's practically on the floor for 90% of full-time jobs.
That is why I propose exactly the opposite regimen from this course, although I admire the writer's free thinking. Return to tradition, with a twist. Closed-book exams, no note sheets, all handwritten. Add a verbal examination, even though it massively increases examination time. No homework assignments, which encourage "completionist mindset", where the turning-in of the assignment feels more real than understanding the assignment. Publish problem sets thousands of problems large with worked-out-solutions to remove the incentive to cheat.
"Memorization is a prerequisite for creativity" -- paraphrase of an HN comment about a fondly remembered physics professor who made the students memorize every equation in the class. In the age of the LLM, I suspect this is triply true.