I think its trivially obvious that die rolls (by themselves) are adiegetic (or whatever term we want to use). However, mechanics and rules in TTRPGs are not simply die rolls by themselves and I'm pretty sure we're discussing those mechanics, not die rolls. If we take as a standard base for comparison the usual declare-decide-describe cycle of an action declaration I think a couple of things become obvious. One, the possible use of die rolls to stand in for fortune isn't really germane to the idea of diegetic or 'in fiction' or whatever. The cycle works both with and without die rolls and the use of a die in cases where the system calls for it doesn't change whether the mechanic in questions indexes something in the fiction or not. When I declare that my rogue will attempt to scale the castle wall we are dealing with an action 'in the fiction' that my avatar could have decided to do. This is the common ground for enthusiasts of immersion and theorists who use words like diegetic as a label to identify actions and mechanics that occur in the rough present of the diegetic frame. Two, this standard declare-decide-define cycle also does a reasonable job highlighting mechanics that seem to escape this notion of 'something the avatar could decide to do'. This second set of possible mechanics is enormously fuzzy but that doesn't mean that people don't recognize them when they see them. I also think it's the case that the idea of 'the conversation' is key to this idea.
The clean diegetic lines of the standard action declaration can become, if you'll forgive a muddy phrase, less diegetic feeling, based on the conversation at the table. Two good examples are Fate points and the Devil's Bargain from Blades - both commonly identified as 'meta' in some way. Both of those mechanics alter the telos of an action declaration by introducing multiple and competing narrative moments within the adjudication cycle. With Fate points I'm specifically talking about the GM proffer version which essentially reads I'll give you this piece of meta currency is you accept X into the resolution cycle. We now have two competing possible realities existing at once that the player (very much not the character) must decide between. The Devil's Bargain is quite similar - an additional die is proffered, increasing the chances of success, with multiple possible realities existing during a short period of negotiation. Again the choice rests with the player and generally escapes the idea of 'something the avatar could decide'. Setting aside for a moment the slippery notion of immersion and what may or may not scaffold it, I think this is a pretty clear moment of difference, a moment where the game pulls back from the avatar to the player and then dives back in after a secondary and interior moment of resolution. I'm not sure exactly how to best capture this definitionally but I think it's one place that words like meta and narrative start to be used in an attempt to grasp the difference.