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Huge numbers of ballooning spiders in Bierbza National Park, with hectares of ground covered with silk. Multiple species in several images.

Quoting teadrivendev's comments:

There are at least four different species here, thus this should be split up into four different observations.

The many little ones with the white spots on the black/grey abdomen are wolf spiderlings.

The large cream-colored one in the first two pictures is probably Larinioides cornutus.

The one with the red longitudinal bands in the first two pictures could be Pachygnatha (clercki?).

At the top right in the first two pictures are two crab spiders, possibly Xysticus.

My first thought was this could be some kind of Fritillary without spots, especially since I saw the butterfly circling a planted Passion Flower, a host plant in California. Then I saw a second, a male who wanted to mate. Then a third. But long story short, they also must be escapees from the Butterfly House here. Per Wikipedia, Dryas iulia are "native from Brazil to southern Texas and Florida, and in summer can sometimes be found as far north as eastern Nebraska." And now also in Leipzig!
Here's the other escapee I saw in the botanical garden, https://www.inaturalist.org/observations/176920329. Otherwise, there were noticeably less insects here than in the Botanical Garden of TU Dresden. I didn't even see a Honey Bee.