Why academics should self publish textbooks
andrewpwheeler.com
andrewpwheeler.com
But I would say, don't use AI for copyediting. Hire a pro with some topical knowledge.
For technical review of the content, I just send it out to other experts.
My above prompt does indeed work well for me, but agree would likely not catch those example errors you list.
OTOH, self-publishing requires some serious time and a skill set, and most modern academics are already working horrible hours for crap job security and pay.
Not mentioned in the article - co-authors (spread the load), departmental support ("wouldn't it be nice to have a textbook that actually fit our syllabus for CS 473?"), and other tricks.