Source?
Deutschlandatlas says that Berlin has whole 2 percent of empty apartments for all reasons, which is less then half of German average [0]
Some of those apartments are being remodeled, some are just in the period where the previous tenant moved out and the next moved in.
There are 16 thousand long-term empty apartments, which looks like a huge number, but it is only 0.8 percent of the total. [1]
Even if those 16 thousand apartments could be all put to market (some have legal barriers, like being part of a complicated litigation), that easing would not last even for a single mayor's tenure. Last year alone, Berlin grew up by 17 thousand people. [2] It was not an extraordinary year.
ALL that money that the Linke wants to sink into old housing should be spent to build new one, just to accomodate the arrivals.
[0] https://www.deutschlandatlas.bund.de/DE/Karten/Wie-wir-wohne...
[1] https://www.berlin.de/sen/wohnen/rechtliches/zweckentfremdun...