Knowing Atahualpa depends on the chronicle but when mercy failed he straight went for terror against the supporters of Huascar so to the elites of Cusco does he offer the same branch he did before to Huascar generals or just goes on film purge mode when he reaches Cusco
What if Atahualpa like Rome actually officially slipts the empire like it's still one empire but now run by two emperors
So based on the character of Atahualpa in the otl really didn't what would he do I don't think he is gonna eye Colombia in 1532.
If he at least spends say the first five years of his rule recovering from the civil war I personally think a nother campaign is possible after all like you mentioned he got his throne via war and a great victory could help his popularity but and here is my question if he successfully conquers at least part of Colombia does he divide the spoils to Quito and his northern base along with Cuzco or just sent to Cuzco to win the nobility over with what he would adquiere
In order:
1. I think the Cuzco elite are screwed, heads will roll, and many families that are nobles through lineage association with past Inca Emperors and their mummies are about to eat soooo much shit. The mummy system is an albatross around the Inca state and I think Atahualpa will be aware of it, in that it's what lets a bunch of people he hates cling to power. I think it's going to be half motivated by revenge, half motivated by administrative reform. Too many reasons to do it and not enough reasons to not do it, not when the last opposing military opponents have been driven from the field and there's no one left to fight on their behalf. Plus as you outlined, Inca justice is very brutal. Atahualpa will be well aware of the Cuzco nobility's perfidiousness if even we are aware of it centuries later.
2. I think it's possible, and might even help boost his legitimacy by doubling down on what Huayna Capac intended. I'd call it very possible, but it's impossible to know Atahualpa would have felt about the splitting of the empire after a civil war. To him it might be the worst mistake Huayna Capac ever made.
3. Agreed. He will have bigger, traitorous fish to fry in the short term
4. I can see a campaign being worth it because of how callous the Inca are towards human capital and its exploitation. Invading the Muisca could be a very easy way(relatively) for Atahualpa to being repopulating his ravaged half of the realm while validating him as another legitimate Emperor through his conquests. I don't think he's sending squat to Cuzco because by the time he's engaging in a northern campaign, the Cuzco nobility will have by necessity already been put in their place. Especially if they put up any resistance as Atahualpa marches south initially and ex. forces a siege of his own theoretical capital. And I think the imperial mummy system is imminently in danger
Forgot to ask how much do you think they can push stop at the musica or push as far as panama Taironas to the Caribbean region of Colombia
5. I think northern Colombia would be a bit of a wilderness and full of refugee groups, rebels, and largely out of Inca control for good long while. They have no reason to value a northern coastline, but would likely become aware of the Caribbean in the process of carrying out their campaign. I'd expect direct control over the Colombian highlands and 'control' over the coasts. The Inca might campaign up to Taironas, maybe even disperse and deport them as a people as they did to many others, but I don't think their control will be anywhere near as absolute as it is/was in the Andes. There's simply too much land, too little resources to control it, and the same methods of control just won't work as well in tropical environments with abundant foliage and wildlife to either lose someone in or get killed by if particularly unlucky. I think the same principles that made the Inca say fuck the Amazon is what will make them say that coastal Colombia is more trouble than it's worth(in the short term).
The more we discuss it the more I'm convinced that an attempt would be likely, it could potentially succeed, but there would be plenty of uncontrollable variables that could make this anything from a shot of adrenaline into the Inca's arm to being the beginning of the end.