Japanese Citypop is great for stuff like this

• Taeko Ohnuki - 4:00 AM with that "LOOOORD GIVE ME ONE MORE CHANCE" in the chorus is just amazing, also Tokai

• Mai Yamane (whose voice you may recognize from a certain track in the Cowboy Bebop if you've watched it) - Tasogare, Wave

• Makoto Matsushita's just great for this kind of vibe, there's the (rather long) Pressures and Pleasures, Love Was Really Gone, September Rain

• Mariya Takeuchi's Plastic Love was mentioned already, so here's another one by her - Secret Love

• Tatsuro Yamashita - Jody, Sparkle

• Akira Terao - Ruby no Yubiwa

• Momoko Kikuchi - Glass no Sogen, Mystical Composer, Night Cruising

• Anri - Mercury Lamp, I Can't Ever Change Your Love For Me, I Can't Stop The Loneliness, Shyness Boy, September Walkin'

• Yoshiko Sai (who's not exactly citypop, I've seen her stuff categorized as Psychedelic Folk, it's weird but really good) - Yoru no Sei, Taiji no Yume

other, non-Citypop stuff:

• some Shiina Ringo/Tokyo Jihen stuff, 能動的三分間, 恐るべき大人達

• trip-hop as a genre can fit this pretty well, here's one of my favorites - [Mysterons by Portishead](https://www.youtube.com/watch?v=slDNOtOQ8oA, this track from Ghost in the Shell: Stand Alone Complex is kind of trip-hop-y as well

• Soviet rock band Kino - Спокойная ночь, Группа крови (this one's particularly somber - the title is "Blood Group", in reference to soldiers wearing a patch with their blood group on their uniforms), Пачка сигарет ("but if I've got a pack of cigarettes in my pocket, then today won't be so bad after all" is a vibe and a half)

• Transistor was already mentioned, so here's something from Bastion

• going into more electronic stuff - The Midnight's an amazing synthwave band, check out The Comeback Kid, Nighthawks, Vampires

• Ed Harrison's soundtrack for Neotokyo is kind of weird, in that it's an absolute amazingly produced OST for a free mod that's pretty much completely dead these days, and it's got great usage of a string section of all things, which you wouldn't expect in this genre, but it just works somehow, and creates an immaculate cyberpunk vibe - Annul, Imbrium, Tachi (the bass in this one is just :chefs-kiss:), Footprint

• some tracks from VA-11 Hall-A's sondtrack - Welcome to Valhalla, You've Got Me, Snowfall, Skyline, Strictly Business

• this remix of a track from the Parasite Eve OST

• the track from STALKER: Shadow of Chernobyl that plays in the bar

• Vampire: The Masquerade - Bloodlines has a few great ones, like the Hollywood theme, and there's some amazing stuff that didn't even make it into the final game, like the alternative Downtown theme

Some of my suggestions are probably not going to fit very well, but I hope you find something you like. Games in general seem to pretty commonly have tracks like this, which I guess I'd describe as having the vibe of "comfy in an uncomfy enviroment" (and thus the combination of grooviness and somberness). I guess they just lend themselves really well to this style - if you have background music that's going to be looping (rather than a more "cinematic" soundtrack that plays at specific emotional moments), you're going to want in to be something chill that you can listen to over and over again without it being too intrusive, but often times the setting/narrative of the game itself is going to have darker elements, so that has to be incorporated into the music as well. There's also probably a ton of jazz that would fit the vibe too.