American universities often have courses designed precisely for this purpose, intended for graduate students who need to be able to read scholarship in language X (often called "X for Reading Knowledge”). And the courses often stick pretty close to the textbooks, which are often written to support self-study. Off the top of my head, there are books intended for English speakers who want to read scholarly French (Sandberg), German (Jannach & Kolb, Sandberg again, and of course this site), and Russian (forget the author, but it was published a while back by Slavica). There are some similar books for Latin and Ancient Greek too, I think, that follow similar approaches. Most of the old ones are like this, obviously, but a few new ones also reject the trend of teaching them as if they were lively living languages.
BUT it's rare to find such books for languages that are very different from English. (Russian and Greek are already arguably pushing it.) Take Japanese, for example. There are courses and lately even some books (e.g. Josh Fogel's) meant for English-native scholars who know Chinese already to get up to speed in reading Japanese faster, but you don't have many (recognizable, at least, without knowledge of katakana) English cognates to rely upon, the grammar is drastically different, etc.
There are no courses that focus on that approach for East Asian languages, but the material exists. Many polyglots are of the opinion that reading-first is the fastest way to mastery. Not to conversational skill, but full mastery. They’ve filled the gaps.
There are good approaches to learning both Chinese and Japanese, but especially Japanese through reading. Start with Heisig to learn the characters, then a source of sentence forms like Kanji.Odessey.2001, then a couple of different textbooks to transition into longer form writing. Then read, read, read for hours a day and never stop.
This is all explained very well in e introduction to the book, which IIRC you can read in the online preview.
Basically learning the meaning and writing of all characters first, then their pronunciation is faster than learning each character fully, one at a time. Experience bears this out.
Beyond the books mentioned elsewhere in this thread, for Japanese, I think the Japan Times published books tend to be good, e.g. Seiichi Makino's grammar dictionaries.
It's more app- and website-oriented, but the Tofugu website has quasi-monthly roundups of new Japanese learning tools.
I feel like Chinese - for a variety of reasons - doesn't have the same high level of pedagogical curation. But the Fuller book is good for learning classical, and Pleco is a great platform for dictionaries, flashcards, etc -- some paid, some free.
The Russian one is likely Reading Modern Russian by Jules F. Levin and Peter D. Haikalis, with A. A. Forostenko.
It is super interesting, as I want to learn to read Russian in order to learn more about the various languages of the region, many of which have only had monographs published in Russian. Now to see if I can find a used/cheap copy anywhere.
But it is a living language and not among the most difficult ones. Why not learn the whole language rather than a reading focus only? You don't have to learn to fluency.
Because of the effort involved. At least for me, learning how to read in a foreign language is far far easier than learning how to understand the spoken language and learning how to produce the spoken and written forms of the language.
So, I can either learn how to read, hear, speak, and write a a single language or I can expend the same effort and learn to read many languages. For me, the later is much more appealing. But then, I'm a voracious reader and too introverted to be interested in talking or writing to actual living people.
Because my main interest in Russian comes from wanting tk read grammars of other languages written only in Russian, as well as other Russian literature. Not much for interacting with others, though of course I'd likely improve that once I met my goals with reading.
BUT it's rare to find such books for languages that are very different from English. (Russian and Greek are already arguably pushing it.) Take Japanese, for example. There are courses and lately even some books (e.g. Josh Fogel's) meant for English-native scholars who know Chinese already to get up to speed in reading Japanese faster, but you don't have many (recognizable, at least, without knowledge of katakana) English cognates to rely upon, the grammar is drastically different, etc.