In legacy quizzes (old quizzes or just quizzes), you open the equation editor, switch to advanced view, and then type \hat p
In new quizzes, the equation editor doesn't have an advanced view, so you'll have to manually invoke LaTeX by delimiting the value with \( and \). So you would type \(\hat p\)
If I had to guess, I would say you're using new quizzes, but it may be the new student experience you're seeing. I'm not used to seeing the "Correct Answer" as a separate tab. It may also be that your Canvas is using some advanced stuff (the Assistance Used section is not a standard feature). Is this on a publisher's version of Canvas or your school's version of Canvas? If it's a publisher's site, they may have a equation palette that is enhanced over Canvas' default and that's how they want you to enter p-hat. It may also be that your Canvas uses the Wiris equation editor, which is more powerful.
I don't use new Quizzes, so I cannot speak definitively about those extra things.
I can speak definitively about the legacy quizzes and for the standard new quizzes.
Using the equation editor works for creating questions and it works for answering essay questions. It doesn't work for fill-in-the-blank questions, where responses must be text-only.
Essay questions cannot be automatically graded while fill-in-the-blank ones can be. Fill-in-the-blank questions have to allow for all of the cases with the old quizzes -- 0.45 is different from .45. There are allowances in the new quizzes.
So, to get questions that allow the student to enter p-hat, the teacher has to manually grade. To get automatic grading, the student cannot enter the p-hat.
One alternative is to use multiple choice questions, where the instructor can use the Rich Content Editor to add equation objects, but then the student picks from the list rather than having to type it.
Your screen shot suggests that you might be a student. If so and you're using questions provided by your instructor (not a publisher's website), I would gently challenge the teacher to show you how to enter the p-hat symbol. They may not know how complicated it is to do so. It may be that you attend a school with instructional designers who took a paper-pencil quiz and converted it to Canvas without realizing the difficulty it would cause for the students. The instructional designer made it look like the paper-pencil quiz and the instructor just relied on the instructional designer to do their job.
You might think that a way to accomplish this would be to use a multiple-dropdown question. Have one for the left hand side, one for the inequality, and one for the right hand side. Of course, the problem with this is that it won't work -- you can only have text responses in drop down questions and p-hat isn't text-only.