I've been thinking about a redo for the Visconti timeline, but I will say this- Ducal Milan is to Renaissance Italy what the Kaiserreich was to Europe. It is rich, urbanized, with a strong industry, noted for its military; with the other European powers at a nadir their arrival would necessarily be marked by serious strife and warfare and I would generally bet on a centralized and wealthy Lombard state being able to come out on top in those contests.
Any Visconti or northern grandee will have strong incentives to expand beyond the northern peninsula- specifically Provence, Naples and/or Sardinia. The Visconti had bad blood with the queen of France, and will desire a royal crown to tie their state together- and conveniently the Angevin crowns are on the verge of a major succession crisis. In fact I intend for Joanna II to wed Gian Galeazzo Visconti and solidify their claims to Provence and Naples as a consequence; this would also give dynastic claims on Achaea and Albania (de facto vassals to Naples on the preceeding century) as well as more tenuous claims to Hungary and Jerusalem.
I would add that an Italy, even a northern Italy, unified in 1402 will almost certainly be capable of going toe to toe with the Ottomans, and meeting them on equal terms, and would be incentivized to do so as the Balkans are their backyard and another source of legitimacy. In practice Italian power would be more ephemeral beyond the Adriatic littoral.
As far as Frederick II and the Sicilians go, letting his uncle Henry survive, so that we have an Imperial Swabian Hohenstaufen line and a Sicilian branch under Frederick, would accomplish much, though perhaps not a unified peninsula. I sketched out a timeline with a "Grand Romania" incorporating Sicily, the Papal territories and the remnants of the Latin Empire and a breakaway Lombard confederation a la the Swiss sndwiched between this and an increasingly centralized Germany.