It will all depend on the new OC and the timing of his hiring.
What I totally expect is that the new OC won't be named until after the bowl game, but whenever he is named, it will likely be someone in house or someone nobody has ever heard of and wouldn't be hired at any other P5 program as OC. In that case, I expect nothing to change. DH will get all the bowl prep snaps and he will be the answer in 2024 for a yet-again injured Cade.
In my fantasy world, the new OC will be named in the next few weeks, and it is someone with credibility. While I wouldn't expect him to take over coaching duties for the bowl game, I think he could at least have a conversation with DH and encourage him to transfer to a D-III school so that Iowa can move forward with QB development for the future. That way ML can get all the bowl prep and play in the Citrus Bowl. I would expect this new fantasy OC to bring in an experienced, talented QB from a G5 program (there are a LOT of good QB's playing at that level) or someone from a P5 program unhappy with his situation for whatever reason. I'm ok with Cade being the assumed QB1, with ML and the transfer being well-prepared to play and/or take over in '25.