What it comes down to is if manga is (or is used as) a count noun or a mass noun. Also, if it is used as a count noun, the interpretation of the sentences relies on how the plural version is spelled.
Lexico (Oxford) defines manga as only a mass noun:
A style of Japanese comic books and graphic novels, typically aimed at adults as well as children.
‘Takahashi is an artist who truly represents the very best from the world of manga’
Merriam-Webster provides both a mass noun and a count noun definition of manga; it also provides different spellings of its plural use:
plural manga also mangas
: Japanese comic books and graphic novels considered collectively as a genre
// The characters' faces beam the big-eyed, manically jolly winsomeness that in anime and manga signals contentment.
— Peter Schjeldahl
also : an individual comic book or graphic novel of the manga genre
// This black-and-white manga is based on the Japanese animated TV series of the same name …
— Library Journal
Macmillan indicates that manga is both countable and uncountable, although it doesn't specify a plural spelling of its countable sense:
Japanese comics or cartoons with stories that are aimed at adults as well as children
Cambridge Dictionary, like Macmillan, gives both countable and uncountable versions of manga, but doesn't indicate a plural spelling for the countable sense:
noun [ C or U ]
Japanese comic books that tell stories in pictures
Much is used with mass nouns and many is used with count nouns.
In some cases, the same word can be used in both senses:
✔ I ate too much sheep. [mass noun]
✔ I ate too many sheep. [count noun, plural with singular spelling]
The context will determine if you're talking about an amount of sheep meat (mass noun) or about a number of animals (count noun).
Based on that, and assuming all of the possibilities of the dictionary definitions given, any of these sentences could be considered correct:
✔ You read too much manga. [mass noun]
？ You read too many manga. [count noun, plural with singular spelling]
？ You read too many mangas. [count noun, plural with plural spelling]
What's correct will also depend on which senses of manga are taken to be acceptable—and, if the count noun sense is, which spelling is used for its plural form.
- If you don't consider manga to be usable as a count noun, then only the first sentence would be considered acceptable.
- If you accept the count-noun sense of manga and think its plural spelling is the same as its singular spelling, then only the first and second sentences would be considered correct.
- If you accept the count-noun sense of manga and think its plural spelling is different from its singular spelling, then only the first and third sentences would be considered correct.
(Of course, you could also accept both spellings of the plural form of the count noun—just as the plural spelling of fish can be either fish or fishes. In that case, all three sentences could be considered correct. It's likely, however, you'd prefer one spelling over the other.)
As a consensus, all of the cited sources agree on the correctness of the first sentence.
Given that different sources seem to say different things about the count-noun status of manga—as well as its spelling—the correctness of the other sentences could be thought of as a matter of style. Or, if not style per se, at least specific to a particular dictionary or use.