That draws attention to what sorts of things one might picture characters know about a saving throw (depending on game text it subsists in)
Their odds, much as you outlined above
What sorts of things influence those odds
That their odds change, depending on what they're evading or resisting
That they experience an evasion or resistance interaction with some things, but not others
That they can learn things that persistently improve their odds
That others can learn things that persistently worsen their odds
If the mechanic is assumed to play out with fidelity in world, then the scientifically-minded in that world could derive the mechanic. They might measure for example that the probabilities are stepped, rather than continuous, say by casting spells requiring saving throws at test subjects.
They might perhaps realise that there is a simple theory that is statistically predictive, despite the myriad of details it apparently elides.
That if they fail to evade or resist initially, they might do so in time.
Alternatively, one could say that the saving throw prompts narration, but does not truly represent anything in world. The problem is then to answer how said narration is constrained, if in fact nothing in world accords with that prompt? How do I say that the mechanic is not possibly diegetic while in fact it successfully predicts what will happen and that seems like something that could observed by characters astute enough. This sort of dilemma leads to sequences of play in games in which characters wryly discuss their circumstances in terms of what they know about the game mechanics.
I'm thinking of moments in the scripts of Red vs Blue, or play at the table when we've been the unhappy victim of system and resolve our sense of dissonance by breaking the fourth wall, or moments when we're just having fun with it. I'm also thinking of the inhabitants of Duskvol's blanket blindness to discontinuities arising from the flashback mechanic. It seems to me that as author-audiences, we choose to act as if game mechanics are generally non-diegetic in order to sustain playfulness. That is, it is part of our lusory-attitudes to maintain a separation between saving throws and what's going on in world. Not because they're not tied together, but because to acknowledge they're tied together breaks play just as much as a cheat or spoilsport does. And there are moments when our play wryly embraces them.