Can someone point me towards a good book or survey article on adaptive/self-tuning of PI controllers?
All I can find online are articles which are either vague or heavy on theory.
This is definitively not a satisfying answer, but what you call "adaptive" in combination with a pi-controller is commonly called
lpv-gain-scheduling (lpv = linear parameter varying). Maybe that helps you find a book.
Typically Self tuning controllers are done in the digital domain. You may want to look into Least Squares Method for controller tuning.