Others will be better positioned to comment on the military aspect of your question, but it's simply not correct to suggest that Poland was less badly affected by the Black Death than other parts of Europe.

I go into considerable detail about this in a lengthy series of posts here, but the bottom line is that the impact of the 1347-50 pandemic on Poland is unknowable, but was very likely greater than is generally thought, while there is no doubt that the country was very badly affected by a second outbreak of the disease that began in 1360. Overall, the best guess we can make, given the limitations of the sources, is that Poland was probably just as badly affected by plague in the second half of the 14th century as a whole as were the states of western Europe.

As for the lands further to the east – both Livonia and Lithuania – unfortunately practically nothing is known of how the Black Death impacted them. We know the pandemic hit Prussia from August 1349, and reached Livonia by 1351; Benedictow lists some of the towns where it is known to have raged, but again nothing resembling secure mortality rates can be extrapolated for Prussian territory.

The economic picture, while also murky, is just a little clearer. By increasing opportunities for the survivors at home, the Black Death does seem to have significantly limited what had been quite a substantial flow of emigrants to the territories to the east. Moreover, it's not unreasonable to suppose that the pandemic also lessened demand for wheat, which was the major export of the territories controlled by the Teutonic Knights. No figures survive to give us details. Neither the Cambridge Economic History of Europe nor Urban's military history deal with the problem in detail; the Cambridge volume states that it's scarcely possible to. A'Barrow, in his recent general work, does list economic problems among the reasons he gives for the decline in the order's fortunes from c.1400, though it is not at all clear that he has either done any significant analysis of the problem, or based his passage on any study that has, so this claim may be little more than another of the unproved assumptions that have long, uh, plagued this field.

The only other thing worth adding to this rather bleak picture is that, while Grunwald/Tannenberg was fought at a late date relative to all this (1410), population figures were a long way from recovering from the impact of the plague even then. The best estimates from the territories to the west where we have more detailed records suggest that, in England, for example, population peaked at somewhere between 4.5 - 5.75m in c.1345 and was still in the range of 2 - 2.5m in 1410.

Sources

Stephen A'Barrow, Death of a Nation: A New History of Germany (2016)

Ole J Benedictow, The Black Death, 1346-1353: The Complete History (2004)

Marian Malowist, "The trade of Eastern Europe in the Later Middle Ages," in Postan and Miller (eds), The Cambridge Economic History of Europe II: Trade and Industry in the Middle Ages (1987)

William Urban, The Teutonic Knights: A Military History (2003)