Tbh the source code of the whole internet would probably be a few PB at most, text is really cheap to store especially because it can be compressed. Images and videos are what makes the premise impossible because even with perfect compression you need an impossible amount of storage to store every video published by mankind.
Yeah but pages are HTML and HTML compresses extremely well. With the latest algorithms you could probably get as low as one byte per page. Probably even better with a decent middle-out compression algorithm.
(Also yes, you are correct within the realm of reality, but not within the realm of comedy.)