Is there anywhere (ideally free online) to find a wide range of reading material that is in extremely simple Chinese, the equivalent of perhaps "Fun With Dick and Jane" in English? https://books.google.se/books?id=Gg9iCgAAQBAJ&printsec=frontcover&dq=fun+with+dick+and+jane&hl=en&sa=X&ved=0ahUKEwiBoZPes5_nAhXuwMQBHYp_DL4Q6AEIKDAA#v=onepage&q=fun%20with%20dick%20and%20jane&f=false
I sometimes read essays written by Chinese children: RuiWang's 作文. They have all levels for free, starting from 一年级 (grade 1).
You can find many English novels translated into Chinese and available for purchase on JingDong or other sites. I read Matilda (玛蒂尔达) this way. I thought it was helpful for improving my reading speed.
You can access Chinese school textbooks for free at 电子课本网: the reading material is 语文. Again, starting from 一年级 (grade 1). [After selecting a book chapter, it looks like you need to scan a QR code, but you can just click it and it'll show you the pages.]
I also note that many books are available for download from Blah.me.
You can search 小学语文 online. There're a lot of Youtube materials. If you're in China, search with Baidu.
I found this one seems quite easy, with English subtitles.
Another free site is https://hskreading.com/ They have short stories/articles at many different HSK levels. They also include the translation, discussion questions, and a hover-over word-by-word translation. I have found them quite useful.
Some non-free e-books are the Mandarin Companion Series (such as https://www.amazon.com/Country-Blind-Mandarin-Companion-Readers/dp/1941875033) and an interesting series that is a simplified version of Journey to the West (https://www.amazon.com/Rise-Monkey-King-Simplified-Vocabulary-ebook/dp/B07SGNCQYX). I have started reading the Mandarin Companion Series (which I find quite useful), but not the Journey to the West series. The Mandarin Companion Series takes Western classics (such as Sherlock Holmes, Country of the Blind, and Emma) and translates them into simple Chinese, while localizing them to China at the same time (i.e. with original Chinese names for the characters and settings in China).