Yeah, it seems to me that Vorinclex is seeking the Tyrite sanctum for immortality reasons but then gets thwarted by Kaya. This would imply Kaya's Onslaught is a story spotlight of a later chapter, probably the final one.
The phyrexians show up on other planes (I doubt Kaldheim will be about a fullblown invasion)
There are still mirrans alive on Mirrodin New Phyrexia
Koth is not willing to give up the mirrans (as far as I understand it?)
Tezzeret has the bridge that allows planeswalkers, inorganic material and organic material coated in special inorganic material (like lazotep) to use the bridge to travel between planes
Karn has retrieved the (Golgothan?) Sylex, able to cause massive devastation
The new Kaldheim native planeswalker Tyvar Kell has the ability to transmute flesh into any material he has access to, temporarily
So what are the odds the following will happen with the plot in the next sets/years:
The Phyrexians will show up in multiple worlds, in small numbers, maybe just one praetor per set. Vorinclex is in Kaldheim, Urabrask may be in Strixhaven etc etc.
Karn wishes to destroy New Phyrexia by destabilizing the core of Mirrodin using the Sylex. Koth does not want to let this happen and after a while they learn of Tyvar's powers and realize they can evacuate the mirrans using his powers and the bridge, which means they'll go after Tezzeret to either force him to cooperate or extract the bridge from his body.
The gatewatch teams up with Karn and retrieve a sample of lazotep from Ravnica or Amonkhet (Amonkhet would be a nice excuse to go back to the plane) for Tyvar to use as a substrate for his powers, turning the mirrans into lazotep and evacuating them elsewhere (Maybe even Amonkhet, they sure could use the numbers to rebuild and the names of the mirrans names were vaguely african to begin with? And there's no overlap in races which means each world can keep its identity.)
Karn then uses the Sylex to destabilize New Phyrexia, destroying the plane and the hub of New Phyrexian activity, though pockets of phyrexians exist elsewhere and Karn, Elspeth, Koth and maybe part of the gatewatch go out to find and destroy the last phyrexians.
The ending even leaves WotC and out in case they want to bring back the Phyrexians again in the future. (Because of course they will.)