> My notebook is full of unorganised notes that I jotted down when a lightbulb came to me one day, rough sketches or mappings of solution ideas, brainstormed lists of features etc.

This is to me the biggest benefit of using pen and paper, but it requires shifting your attitude towards pen and paper to treat everything you write as disposable. Just freely sketching out ideas and using paper as a place to dump thoughts without concern for quality, formatting, or even having them be cohetent, is probably the most productive way for me to solve problems - so much so that I have switched to using large post-it notes, rather than a notebook. The good notes stick around for a few weeks, and the bad ones go straight into the bin.