Wow, thanks everyone for so many replies, suggestions, and empathy! I'll try to reply directly to a few when I have a moment but for more context:
I read all kinds of books with her; lift-the-flap, like the popular bunny hunt books, counting books, like 'Little Houses', Usborne poetry, knights of a the round table stories, The Library Lion, Sophie's Hat, How Does It Work? Monsters and Beasties... 'Her' books are books aimed at children one to eight years old, roughly speaking, though the older ones are usually fact or fairytale books so they still have lots of pictures. She likes predators and anatomy a lot, but not as much as 'Where's Mr. Unicorn?'.
Her speech is fantastic, and she will read most of the books alongside me, or quote them if we say a word that appears in one of them (for example, our neighbours are having work done, and when I explained to her that the loud noises were power tools, she rattled off three pages of a construction book I rotated out two weeks ago). She absolutely refuses to read to me, though will pick up and read the book herself if I'm too busy. We do all the book variations (how many butterflies can you see? What colour is Mouse's jacket?), and she really engages by asking about things she doesn't recognise, or pointing out things that she does, be that letters, nouns or saying "Oh no, Crocodile sad", "Mouse fell over, he sat on thistle!".
We have letter/number blocks and beads that's she adores, and it has affected her drawing in that she only wants to draw circles and letters. She insists that I write specific words for her, and is very insistent that she wants the word, not just the picture, when I try to encourage drawing images instead. I've written the words 'Mum', 'Dad', 'Cat' etc. so many times in the past month that it could cover the walls of a padded cell and look the part.
When I say 'my' books, I should clarify that I have an eclectic but non-fiction oriented bookshelf, so that includes art books from movies and video games, Lots of myths and British folktales, lots of encyclopaedias and guides about everything from wildlife and plants to dinosaurs to Egyptian tombs to heritage crafts to the history of medicine - she just pulled my 'Maps of Middle Earth' book off the shelf before I started typing, and has shown a reasonable amount of interest in 'An Illustrated Guide to British History' as well as my current audiobook about the ethics of archaeology. I guess she likes the authors' voice more than the content though :P
Most nights my husband will read fiction classics for all three of us, things like Harry Potter, LoTR, or, currently, I, Robot. She likes drifting to sleep while he reads, assuming she's not too interested in pointing out letters she knows. Though this ritual often takes some tears because she'd rather read 'Belinda Goes for Gold' for the nth time instead.
We go to the library about once a week, having skipped recently due to illness. We do check out a few books every time we're there, but they mostly go untouched above the at-home favourites. She mostly enjoys running around the library and saying hello to everyone, so not much reading happens while we're there.
Apologies for the long post! I'm thrilled she's so interested in language, and I know just how lucky I am to be able to support that, as well as knowing how important it is for her to go through the same books over and over. I just wish there was a way to not be so bored; definitely a me problem!