At this point, I think the best-case scenario for Rune is that he has a surge sometime in the next 5+ years and plays consistently well long enough to capture a Slam, even challenging for the top of the rankings if the context is right. If he has that surge, the confidence might give him a nice run of a year or three in which he's challenging the Sincaraz Dynasty.
He's still young enough that this scenario is a possibility, but my main point is that I think the dream of a new Big Three has faded to the point of oblivion. This has probably been clear for a while now, but now seems crystal. Or rather, he's no longer the main contestant - Fonseca is the guy we should dream on. And to be honest, I think Rune is more in a group of guys including Draper, Mensik, and maybe Musetti, Fils and Shelton, who are and/or will be the new "second tier" going forward. Rune has the physical gifts, but not the mental template, imo. I think he's got the highest upside of those guys, but that doesn't mean he'll have the best career.
So if we were to imagine the tour in June of 2027, two years from now, I think we'll have Sincaraz on top with Fonseca rising to join them--either as an equal or not far behind--and then a big step down to Rune, Mensik, Fils, Draper, Musetti, Shelton and maybe one or two others. That talented "second tier" group will be jostling for places in the top 5, spare Masters titles, and maybe the occasional Slam, with Next Gen fading in the rear-view.
And of course there's always the possibility of someone else emerging - which is always an inevitability, but just a matter of who and when. For the "post-Fonseca" group, so far Cina and Engel have caught my interest the most, though there are other names to stick a pin in (Dedura, Blanch, Hewitt, etc)...but we're a long ways away from knowing who among that group will emerge as a player to watch.