I know you’ve got plenty of suggestions already for Goodnotes but I thought Id throw in my opinion. I’ve found for math there is nothing better than having infinite space so I live with OneNote. Plus, it instantly syncs with my PC and I can view notes much easier. The iPad screen is so small it gets tiring panning around and reading notes off of it. I missed being able to have a ton of pages all sprawled around me so OneNote is my best option to replicate that

For annotating pdfs or working on strict worksheets I put it into Notability. This syncs with my Google Drive and its otherwise pretty reliable. I think it is far better than Goodnotes (especially for drawing diagrams and straight lines cause it has some assist thing it does)

And for the file transferring there are plenty of workarounds. If you’re familiar with AutoHotKey, I have a couple of scripts that allow me to sync my PC clipboard over to the iPhone and also send screenshots and PDFs between them with the help of Apple Shortcuts.

If you want to take notes on an iPad I think OneNote is probably best and theres workarounds to get things working how you want. Though, consider the size of the note taking screen because I find my 11” iPad too small. Hope this helps!!