Even treaty of Welawa didn't abolish EVERY single tie between Polish crown and Ducal Prussia
"Single tie" is meaningless term. Prussia became a sovereign state on some conditions.
and in it's decisions were points like: after death of last male-line Hohenzollern the Duchy should be incorporated into Crown, the Estates of Prussia still had a right to ask Polish king for help when they liberties were thought to be broken
Whatever was there it ceased to exist in 1663 when they swore allegiance to
Frederick William I.
and the estates were supposed to make homagium after coronation of every new Polish king.
"In case of the extinction of the
Brandenburgian Hohenzollern dynasty in the male line, it was agreed that the Prussian duchy should pass on to the Polish crown.
[20]Owing to this clause, the
Prussian estates were obliged to pay conditional allegiance to an envoy of subsequent Polish kings upon their succession ("
hommagium eventuale, Eventualhuldigung"), while they were released from previous oaths and obligations regarding the Polish crown."
https://en.wikipedia.org/wiki/Treaty_of_Bromberg#On_the_status_of_Prussia
Which is not exactly the same thing as you implying.
For all practical purposes and for the outside world Prussia became a sovereign state which allowed Emperor Leopold to recognize Elector
Frederick III as "King in Prussia".
So when PLC was starting it's union with Saxony ties with Prussia weren't nonexistent at all.
Of course there were ties: they were neigbours and there were some territorial issues like one of Elbing but Brandenburg-Prussia was quite free in its foreign policies (for example, remained neutral during the Russo-Polish War of 1654–1667 and it did not even sent an envoy to the inauguration of the Polish king in 1698.
I was not talking about formation. I was talking about it's rise to status of one of major European powers.
Well, short of your wishful thinking and semi-imaginable "relations", I don't see how this could happen in the world close to OTL.
Not only effective military systems are coming out of the blue, but empires also aren't coming out of the blue. So I'm waiting for your explanation why rise of Russian Empire was inevitable.
As usually, bad quoting. I said that creation of the unified Russian state became pretty much inevitable since the reign of Ivan III. With the GH gobe as a dominating regional power there were very few things which could prevent this process.