Thanks for the clear explanation, Tim. The reason why I could not understand the OP's problem is that I never ever create Questions from inside a Quiz, I always create my questions in the Question Bank first and then add them to a Quiz when I create it.
I have just tested the 2 methods you mention in your post and now I understand. I expect the OP used method #1, which explains the problem he has, and I have to apologise for not understanding him.🫢
You write "Up to Moodle 4.5, the default was to do 2., on the theory that it would promote reuse. That is, if you added a question directly to a quiz, it would go in the course question bank. That is about to change." How is that going to change? Where ? in Moodle 5? But if the change means that method 1 will be used by default, then it should be made very clear that duplicating a Quiz created with method 1 will result in the problem mentioned by the OP, no?
Using the core Moodle H5P activity works only using method 2. You first create H5P contents in the Content Bank, and then on your course page you create a H5P activity into which you place a H5P content from the Content Bank. This seems sensible and logical to me... or not?
When making a cake there are 2 methods:
method #1: you decide on what sort of cake you want to make, you look at a recipe, you look in your cupboards and fridge to gather the ingredients and you make the cake.
method #2: you look in your cupboards and fridge and, based on what ingredients you have, you try to find a recipe which use what you have.
Not sure if this metaphor applies to Moodle Quiz making, however.😵💫
