Yesterday, I had thought that we might wait a few more days to book accommodation in Germany. But I had a quick look through AirBnb and came across an inexpensive one that caught my interest. I sent the host a couple of questions, which she eventually answered, but by the time I went to book it, somebody else had already done so!
So, while there are lots of choices available in Berlin because tourism is down and the weather is quickly cooling off, the good ones still do go quickly. I figured I had better spend a bit more time looking for one that is suitable for us.