There are a bunch of "news sources" online all with very similar articles, and not one lists where you can sign up.
The article mentions Eisenhüttenstadt. That's at https://www.xn--jetzt-plne-schmieden-izb.de/probewohnen/ . Applications due 5 July. Still time!
I also mentions Frankfurt (Oder). The link I found at https://www.frankfurt-slubice.eu/de/arbeiten-leben/probewohn... says it was September 2021 to December 2022.
I think https://stadt-auf-probe.ioer.eu/wohnen/ is another, in Görlitz. I found no date.
I wonder how many people were involved in creating the project, the website and the forms, then selecting candidates.