Just an idea I was thinking to use in my TL: if Sigismund Vasa had died in 1587 after his landing at Danzig but before the
battle of Byczyna (for example, if at the time of his arrival Danzig is being affected by a plague and he dies) how would it affect both Poland and Sweden? Would Archduke Maximilian be accepted as king? And in Sweden, assuming that John III and his wife still have a male son born around 1589 (IOTL he would be
John, Duke of Östergötland ) would this three years old boy be accepted as king or the throne would go to Duke Charles ?
Off the top of my head, the Polish faction probably still wins and will put forward Anna Vasa (Jadwiga can do it after all so its not without precedent)
Sweden could still go to Karl though he may prefer to be the power behind the throne leading the regency of the 3 yr old John.
That insures no dynastic union....whether she returns to Catholicism publicly but favours Lutheranism privately I guess would depend on how badly she wants to be "Queen of P-L" Protestantism will probably gain a measure of acceptance under her rule. NO wide spread embrace of the counter -reformation. But she won't tolerate religious discord either.
Anna will of course have to marry. She can as Queen marry Brahe, but it may not be the best for P-L.
Poland and Sweden could remain allies though perhaps with a Vasa on both thrones. Karl may have disliked Anna but as long as John is alive and he is regent It would not be a bad thing to have a relative on the throne in P-L favourable both to protestantism and capable of lending aid against Russia if need be.
As to plague in Danzig, wouldn't Sigismund simply land in Konigsberg or Elbing instead in that case.
Just another thought, given that Anna is Lutheran, Would the Polish faction not ask Anna Jagiellonska to rule alone until a suitable replacement can be decided on by the Polish faction. That would then give her time to work on Anna or at least convince her of finding a suitable co-ruler if she were to be put fwd with her support at her death. There is a few years here afterall...and will Anna Vasa may not have countenanced marrying anyone other than Brahe, there is the draw of the throne and the direct influence she can wield as ruler of the Commonwealth...