This is Berlin! Too little rain? I don't think so.

The problem you are talking about is different and can be solved with traditional means (i.e. sprinklers) if needed. But due the fact the prior rain water is present on site for a longer time instead of being drained off in sewers they may not need to run the sprinklers as often (another benefit!)

What generally happens to most wild plants during the summer? Most of them can survive a few dry spells.

Berlin was a sump before becoming a city, it still has ground water almost up to ground level in some areas. Has a bunch of pumping stations to lower ground water, too.

The grass areas will need occasional watering in the summer, but most of the plants shown look like robust native species that can survive summer without problems

The suitability and cost of the technique will vary by climate.