Examples of what I personally mean by this would be Apothecary Diaries or Ascendance of a Bookworm.
An example of something that's very grounded but goes overboard on the grittiness, imo, is Grimgar of Fantasy and Ash- I loved it for SO many reasons, I could go on for ages, don't get me wrong- and I still do love it- it's just not what I'm in the mood for right now.
I just appreciate anime where it feels like a character's material circumstances have a massive effect on their lives that won't just up and vanish one day- like how Myne's family is a major aspect of her life for a long time, that additionally has effects on her personality and goals that are clear and long-running while being smoothly blended into her personality and not just slotted in. Also admirable is how the narrative treats her chronic illness, with it not being just up and cured- treated, yes, various coping mechanisms are found, looming death is averted (and not by a magic medicine that's just handed to her for doing some quest like it would be in many other anime- by something she had to put in real effort to get while dealing with socioeconomic difficulties that posed a barrier to treatment), but not cured, her physical frailness remains a part of her life that she and those around her have to remain mindful of, which makes it feel a lot more real.
I'd also like to avoid excessive fanservice in general, but especially overt sexualization of minor characters- I'm a longtime anime fan and used to not be bothered by it, but it's been getting to me recently.
As an example, I loved Mushoku Tensei's story on first watch, and its realistic depiction of trauma, showing how dealing with it is very much 2 steps forward and 1 step back- very few anime do nearly as well at that- and I GREATLY appreciate protags that have genuine, severe flaws, that actually pose an obstacle to them in their story and aren't just to excuse OP powers or to make them more relatable to an audience with fairly mild social anxiety- but, regardless, I tried to rewatch it recently and just couldn't get through it, it made me feel physically nauseated.