The {\it AGORA} High-resolution Galaxy Simulations Comparison Project. VIII: Disk Formation and Evolution of Simulated Milky Way Mass Galaxy Progenitors at $1<z<5$

We investigate how differences in the stellar feedback produce disks with different morphologies in Milky Way-like progenitors over 1 $\leq z \leq 5$, using eight state-of-the-art cosmological hydrodynamics simulation codes in the \textit{AGORA} project. In three of the participating codes, a distinct, rotation-dominated inner core emerges with a formation timescale of $\lesssim 300$ Myr, largely driven by a major merger event, while two other codes exhibit similar signs of wet compaction -- gaseous shrinkage into a compact starburst phase -- at earlier epochs. The remaining three codes show only weak evidence of wet compaction. Consequently, we divide the simulated galaxies into two groups: those with strong compaction signatures and those with weaker ones. Galaxies in these two groups differ in size, stellar age gradients, and disk-to-total mass ratios. Specifically, codes with strong wet compaction build their outer disks in an inside-out fashion, leading to negative age gradients, whereas codes with weaker compaction feature flat or positive age gradients caused primarily by outward stellar migration. Although the stellar half-mass radii of these two groups diverge at $z \sim 3$, the inclusion of dust extinction brings their sizes and shapes in mock observations closer to each other and to observed galaxies. We attribute the observed morphological differences primarily to variations in the stellar feedback implementations -- such as delayed cooling timescales, and feedback strengths -- that regulate both the onset and duration of compaction. Overall, our results suggest that disk assembly at high redshifts is highly sensitive to the details of the stellar feedback prescriptions in simulations.