you can't go looking for a one to one comparison. the equivalent is going to be mostly well animated adaptations of successful seinen (and some shonen or shoujo or josei that fits the bill) manga. even if they aren't as grounded as breaking bad, they'll still hit that spot comparatively. this is where erased and monster are. things like the recent chainsaw man anime might count, as well as upcoming anime such as dungeon meshi and pluto (based on a manga by the guy who did monster). older examples might include mushishi, space brothers, ghost in the shell: sac, possibly kaiji. jojo part 7 might actually qualify (though none of the previous ones would)

original anime are trickier but some that come to mind would be things like oddtaxi (which i think fits all your criteria), violet evergarden, paranoia agent, maybe a psycho-pass or anohana. if you're willing to get a little more out there you could include more experimental stuff like the works of ikuhara, or lain or princess tutu. and some big franchise stuff like woman called fujiko mine or gundams like 0080 or ibo might qualify as well

i haven't watched everything i mentioned here, but my understanding is that they're all relatively sober, serious works that have thematic content not normally seen in your demon slayers or isekai of the seasons. most of them are fairly melancholic in tone, and though almost all are scifi or fantasy they take a somewhat grounded approach to the subject matter and aren't power fantasies. (the ones i mentioned as being experimental might not fit this, but they're good enough i needed to mention them).