The "Annie" in the opening school scene is the original Annie, Oliver Warbucks's daughter from the comic strip.
Assuming that Will Stacks and Oliver Warbucks did exist at the same time, and since the comic strip does live in, well, Comic-Book Time, the Annie in the opening scene isn't merely a throwback to the old films, but rather the old redhead Annie besides Stacks' future adoptive daughter. It just so happened that Annie Bennett-Stacks happened to have a remarkably similar Cinderella story as with the other Annies and lived alongside Warbucks' daughter. Annie can't read because she has dyslexia
Annie is shown reading a bit. She reads the note to the kids, reads the SNS form, and navigates around the city, which would require a bit of reading. But she would struggle to read things quickly, like on the teleprompter, and would likely feel overwhelmed trying to read long paragraphs, like in the background check. People with dyslexia can read, but most need extra education to overcome it, and Annie likely slipped through the cracks as she probably learnt to not show weakness growing up in the foster system, hiding her struggles with reading.