Yeah, I'm getting my Master's in modern Korean lit, I have some suggestions.
Modern East Asian lit, as far as I'm aware of it from my few Asian lit classes, it is focused on short stories and essays. For China there is the author Lu Xun (probably China's most famous modern author) and his short stories A Madman's Diary and The True Story of Ah Q are probably his most famous. His work is largely political satire and uses a lot of symbolism. You could probably read a ton of his short stories in a single day, but I recommend finding some explanations of their context because, as mentioned, they were really political. The Gate of Heavenly Peace is a non-fiction telling of Chinese modern history that does an excellent job contextualizing modern Chinese writers. If you want to get into modern Chinese lit I think this would be a great place to start so you have a general understanding of the vicissitudes of history and the place of Chinese literature therein.
For Taiwan, Huang Chunming's The Taste of Apples collection of short stories would probably be a good place to start. There is also a movie of vignettes called Sandwhich Man which features a film adaptation of The Taste of Apples. I very highly recommend the movie Yi Yi. This family epic follows the lives of a middle-class family in Taipei (I think Taipei) and it is truly a beautiful story.
I don't know much about Japanese literature, so I'll let someone else answer that.
I recently gave suggestions for modern Korean lit on a similar sub, so I'll just copy-paste that in here:
These first three books were bestsellers and are some of the most well-known when it comes to contemporary Korean literature:
The Vegetarian by Han Kang won the Man Booker and was a best-seller, but you don't read much about Korea in this book. It feels like a book full of close-ups. It follows the main character as her mysterious choice to become a vegetarian begins unraveling her life and relationships.
Please Look After Mom by Shin Kyung-suk, a best seller in Korean and abroad(maybe?). This follows the story of a family whose elderly mom went missing on her trip from the countryside to Seoul. As they look for her they do some soul(get it?)-searching of their own.
Pachinko by Min Soo Lee. This epic saga follows three generations of a Korean family and is set primarily in Japan during and after the Japanese occupation of Korea. Though the setting isn't Korea and the author herself is Korean-American, this book was an intimate look into the lives of Korean-Japanese people and the historical legacy and pain of modern Korea. It's also beautifully written.
I would consider those three as relatively lighter and contemporary. AS bestsellers they're also probably the easiest to pick up and be drawn into. They're my generic recommendations to people looking to read their first Korean novel. The next few books are more "classic." These are considered required reading in Korean high schools and I think they do an excellent job at offering a glimpse into Korean society from various points in time.
I hope these recommendations are helpful, if you want more I could be happy to give you more. My one note is that long fiction is not very popular in Korea, instead short stories dominate the market. If you want to read excellent translations of contemporary short stories I recommend the journal Azalea. They sell used copies on Amazon for cheap, or alternatively I think you can download pdfs for free online. Azaelea prints mostly contemporary short fiction and poems, but they do occasionally visit other modern authors and present critical essays. It's a great journal if you are interested in getting a more anthological look at what Korean literature has to offer.
South Korean authors that are being translated now are Kim Young-ha, Han Kang, and Bae Suah(she writes in a more stream of consciousness manner, but her translator Deborah Smith is a bit controversial for being unfaithful to original texts).
If you can find someone with institutional access to get this story, Needle, is my favorite Korean short story and I highly recommend it. It's very well translated here. I have the physical journal, but no access to Muse currently.