I can't speak to the 300k number but an increase in readership is plausible because I saw how reducing friction to consume a book can massively change reading habits. E.g. my friend with the new Kindle finally got around to reading the classics like "Madame Bovary" and "Anna Karenina" because she could get ebooks from Amazon for $0.00 (or sometimes a tiny amount like 95 cents).
The previous existence of those public domain books on Gutenberg Project's website was irrelevant since the HTML or TXT files weren't easy to consume unless one printed them out on a printer.
Yes, public domain books have always been sold on Amazon as real paper books but the shipping would end up being $3.99 even for a book costing $0.00.
The Kindle e-reader was the technology to enable her to read public domain books for free with minimum friction. (Even a trip to the public library to check out and later return a physical book for "free" is too much of a hassle.)
I can see how this NYPL project is trying to make a friction-free book reading experience for Instagram users who already own their smartphones. No Kindle purchase necessary. (In my other comment, I mention how millions of Chinese people are reading books on their smartphones.)
You mention a friend who read chose to read "Madame Bovary" and "Anna Karenina" upon discovering a cheap and convenient e-book format. Those books are classics in the Western Canon, yes, but they are also slogs, by some measures.
The other thing that happened, and continues to happen in parallel with the explosion of e-reading tech, is an explosion of other things to (copyrighted) read, written in the modern colloquial, (perhaps more) relevant to modern times. The rise of the tepid, self-published novel on Amazon is the best example of this.
I can believe that there is a latent desire out there for more good books to read or a cool new tech to use to read them, but I doubt very much that very old books in the public domain sate that thirst in any significant way. I think your friend is in the minority.
You are not. Instagram is likely set up to count views of a post, not full reads.
That there are 300k people who are now suddenly "reading" books that have been available in a huge variety of formats in the public domain for years because they show up on Instagram?
Show me the actual usage data. How many of these 300k got past page 3?
The design is nice, the presentation is good, yes, but I doubt very seriously the existence of this hidden, neglected population of bibliophiles.