I think it's probably pretty likely that they want to both save as many innings for later and also not create immediate pressure for a callup. That's putting the cart before the horse a bit, but if he takes the current performance and replicates it over 6 or even 5, well... Bailey Falter is starting tomorrow, not hard to see where that would go.
Skenes with 3 here, maybe 3 again or 4 in the Indy opening homestand next week and the following start. If he's at 5 and dive for the second Indy homestand (4/16-21), that gives you maybe a couple starts like that, then a couple where he's pushed a bit more, but it wouldn't surprise me if 5 or 80 pitches is a de facto limit for a bit, even if he's promoted pretty quick.
Hard to say now, and not worth speculating a ton about after just 3 innings. There may be a period where he has some scuffles, but I sort of doubt it. Looking at the schedule, it's hard not to envision a situation where he is called up by the end of May. The biggest red flag I can see is that the NL ROY race could very well be open enough that he could enter in with a strong enough performance. Yamamoto seemed like a sure thing, but if he has a couple month adjustment period to MLB, it might open a window, and in any case Skenes would only need to finish second for the service to accrue.
Hopefully they just have a plan that's focused on the pitching itself, and positioning him for as strong a professional debut as possible. The rest is noise because this guy is massively important for 2025 and beyond, no matter what happens this year.