Italy is a mess, in the immediate - it's just bled dry by WW1, and OTL they had put all naval construction on hold before the treaty even existed. Up to 1925 nothing changes significantly, I expect - maybe the Caracciolo isn't actually scrapped, but it sure isn't getting completed.
Afterwards, things can get a bit better. Maybe the Caracciolo is completed as carrier (as had been planned), which is going to be a general boon for the RM - Italy was a pioneer in air warfare, by this point, so naval aviation might get a reasonable push from that. The real issue is Mussolini, because Fascist governments always have a fantastic hard-on for battleships: even Japan balanced Pearl Harbor with building Yamato and Musashi. But if, just if, that can be avoided, Italy could go in OTL Japan's footsteps for much of the same reasons: carriers are cost-effective, battleships are very much not, and Italy needs cost-effective stuff in order to remain competitive.
Another butterfly is (sadly) no Zaras as we know them - the whole reason for building them doesn't exist. Might get uparmored Trentos at some point, but they won't fight Wichita for best-armored CAs of WW2.