"or for simple quizzes that can be graded automatically"

I remember at least one test like that when I was at school (in the early 90s). There was a special printed form with places where you would mark your answers (to multiple-choice questions) by filling in rectangles with a pencil. These were read by computer.

Of course, this would be even easier to implement now. No need for students to carry computers or a fancy SPA to administer the test.

(Assuming you don't need adaptive testing.)

Even so, why would you allow students to bring their own devices? Just provide some terminals managed by school IT.