I know this is explicitly a D&D thread but I'll just mention very quickly that right now my favorite approach to what you're talking about is how some PbtA and FitD games do XP triggers. These are explicit rewards for players doing specific things, that they decide whether they deserve based on play, rather than hoping for the GM to approve. In Brindlewood Bay, for example, at the beginning of each session you pick from a list of End of Session Questions, such as:
-Did you dote on someone?
-Did you show someone that you’ve “still got it?”
The XP triggers directly encourage you to find opportunities to do certain things, which in part reinforces the premise (that you're playing old lady investigators). It's the kind of mechanic some would consider too "gamey," but the result (from my experience) is players getting into more narratively interesting and entertaining interactions. And, more important, not focusing on efficiency.
Blades in the Dark does a similar thing, based on playbook. So for the Leech, your per-session XP triggers are:
You addressed a challenge with technical skill or mayhem.
You expressed your beliefs, drives, heritage, or background.
You struggled with issues from your vice or traumas during the session.
Now you could imagine someone being a certain kind of someone and always tossing out some tidbit about their personal code, and also moaning about their addiction for 10 seconds, and then happily checking off those boxes. But the game trusts that perhaps that person won't stay so shameless throughout, in the face of eye-rolls from fellow players, and also even if you think you're gaming the system, you're at least doing more interesting or surprising things than you might have, particularly if you're compelled to unleash mayhem but the score demands subtlety, or you're desperate to use your technical skills despite the need for speed. The XP triggers can encourage you to act in ways that aren't always in your best interest. That's about as close to pushing people to play to their characters' humanity as I've seen.