Sigismund was not the most talented son of his parents (but still way better than Vladislaus) but certainly healthiest one. He inherited iron health of his grandfather (and not only this, just like his male line ancestors all the way to Algirdas, Sigismund abstained from alcohol, which was quite unusuall for that time and place). Despite being fifth son, he eventually outlived older brothers and get thrones of Poland and Lithuania, and, despite being forty years old at the time of his coronation, he still ruled for over four decades. So lets say his reign lasts even longer: ITTL his older brothers John Albert and Alexander die during late 1480s (at the very end of decade, just before death of Matthias Corvinus). Thus there is no fight between Jagiellon brothers over Hungarian throne. Casimir IV from the very beginning would support claim of his oldest son Vladislaus and there would be no other Jagiellon candidate for the throne in Buda. As result Vladislaus would have stronger position in Hungary and would not need to make deals with Maximilian Habsburg like IOTL (IOTL Vladislaud had to compete for the throne with John Albert, thus to secure his western flank he promised to make Max his heir if he dies without sons). Perhaps in such situation Vladislaus would not even need to marry Matthias' widow Beatrice of Naples (IOTL he needed her money to pay mercenaries from Black Army to fight John Albert's army).
Casimir IV would have only 3 sons upon his death in 1492. Vladislaus is King of Bohemia and Hungary already while Frederick is bishop, so Sigismund would be obvious heir in Lithuania and obvious winner of election in Poland. If he lives as long as IOTL he would spend 56 years on the throne, more than father and grandfather. Thus, he would have a lot of time to consolidate his power. How would his extended reign looks like? Compared to John Albert, Sigismund was less warlike (John Albert was exception among generally peacefull Jagiellons) and from the very start of his reign he has both Poland and Lithuania under his rule (John Albert and Alexander were in worse situation after 1492 IOTL). Sigismund would not face such problems like Alexander did after death of John Albert, when he struggled for Polish crown. Thus there would be no need for somethig like Mielnik Priviledge and then for
Nihil Novi (Alexander IOTL needed
Nihil Novi to counter Mielnik Priviledge. Mielnik Priviledge, which was never implemented eventually, made King pawn of magnates from Royal Council,
Nihil Novi in turn stated, that to create new laws there is need for it to be accepted by Sejm (King, Senate and Envoys). Sigismund I even after
Nihil Novi marginalized House of Envoys and ruled through senate (senate was smaller and King had right to nominate senators, unlike envoys, who were choosen by nobility, thus senate was easier to control). Without
nihil novi and with more time, co-rule of King and senate and marginalization of House of Envoys should be even stronger.
Also, it is interesting how would relations between Sigismund and Mikhail Glinski looks like? IOTL Sigismund spend few years before succeeding Alexander on Polish throne in Silesia and Hungary and unlike Alexander, who was Glinski's friend, he was not very close to him. Maybe IOTL Glinski would not have reason to rebel like IOTL, when Sigismund, not familiar with situation in GDL after spending few years abroad, pissed of Gliński, taking side of his rival Zabrzeziński?
@krieger