Nope. Your article was for the first half of 2020. For the whole year of 2020, the numbers were down again, fourth year running.

"16.03.2021: Heute hat das Amt für Statistik Berlin-Brandenburg die Baugenehmigungszahlen für das Jahr 2020 veröffentlicht. Die Zahl der Baugenehmigungen sank in Berlin das vierte Jahr in Folge."

https://www.immobilien-aktuell-magazin.de/topics/auswirkunge...

https://www.rbb24.de/politik/beitrag/2020/11/berlin-mietende...

And the effects already started in 2019, when the law was planned:

https://www.zeit.de/wirtschaft/2019-11/berlin-mietendeckel-g...

If it's been happening for four years, how did the Mietendeckel cause it?

In 2015, a similar but less draconian "Mietpreisbremse" was enacted at the federal level. 2016 was the year the construction trend turned from yearly increases to declines, and it has been declining consistently ever since.

In 2019, in anticipation of the Mietendeckel, the decline became significantly steeper.

Several large companies announced that they were halting all new construction and renovation projects.

At the same time, inventory has practically disappeared. So instead of "unaffordable" housing[1] for new tenants, we now have no housing for new tenants. (Existing rents were already protected).

[1] Berlin is still cheap compared other large German cities and certainly compared to most capital cities of industrialised countries or places like SF. It's just not quite as ridiculously cheap any longer.