Thank for your response. To be honest, I'm not sure what I version I was running before as it was a school device (I'm a teacher). I updated only because my screen recordings weren't recording audio, even though I had the microphone on (update fixed this issue). I imagine it was a recent iOS because the teachers got the iPads last year and this was the first update I've had to do. I can't comment on if this works before as I had literally only just discovered this feature.
It was through using the MarkUp function, not inserting a sketch into Notes. So I would just draw on the note normally, save the image to my iPad and when I inserted it into another app, e.g. Google Slides, it had a transparent background. I was using it to make clipart; in fact, the screen recording I was doing was a tutorial to show other teachers how to make clipart with a transparent background to use! I still have that video saved, and have attached some pics below to show a drawing in Notes and what it looked like in Google Slides against a coloured background. I went to complete a new screen recording with audio working, and that's when I saw they now have a white background.
I'm not sure if it's just a glitch or if this is something new, but hoping it's the former and can be fixed! I don't know why they would change this great feature.