There are some great comments and discussions there.
I ended up buying the Casio fx-991 ES PLUS as a result.
Includes beautiful UI (roots, exponents and fractions are displayed like we write them, so more is visible, and the navigation is easier), spreadsheets, printing out values of a real function, solving any real equation for X (one solution at a time, gotta give it different starting Xs for optimization, though), some very basic probability (Gauss) statistics (e.g. linear regression), up to 4x4 matrices, finding derivative in a point, sum over a range, integral over an interval, arithmetic with complex numbers etc.
It doesn't render graphs, but, it renders a qr code that a phone can scan and then the phone shows the graph, so some graphing is there for studying, but not an exam.
Practically speaking, I probably would have been better off getting a much simpler calculator with bigger number buttons. But I do love the aesthetic of the scientific calculator, it seems to hold so much potential.
This fits your checklist I think: - notably more intuitive than the classical Texas Instrument / Casio - calculations input are shown - ( not that it seems to matter for you, but it also has python on it )
It's like the FX-991ex mentioned elsewhere but it remembers more things and has history and a display that is decent.
I own one and have been using it for a couple of years now.
Many consider its TI nSPIRE successors to be flawed.
Avoid TI-83/84, despite fancy-looking backlit screen and smartphone-inspired UX, they are ultimately the successors of TI-82, the "high schooler" stripped down functionality version of the TI-85.
It has to show input and output at the same time (or at least full input), be ergonomic (backlight, nice keys) and not looking childish.
Right now I’m borrowing my SwissMicro RPN which is awesome gadget but outside of complete overkill - its not backlighted display is hard to read.
Context is that the kid has very short working memory. Whereas they understand the concepts really well (I help with tutoring) due to frequent mistakes and forgetting numbers mid-flight the grades are awful which negatively impacts attitude etc.
I noticed positive impact with calculator because not only they start to memorize some basic calculations, they also start to feel general result correctness based on those visual inputs.
As mentioned before - SwissMicro works but maybe there’s something with backlight and not RPN based. It has to be calculator not an app because I hope to convince school to let them used daily.