The tweet I was responding to, talks about the doubling time, in answer to the question "is it slowing down". She says "still about 2 day doubling", with the implication that it would be slowing down if the doubling time was becoming longer.
So, the rate of growth of the rate of growth is what we're talking about isn't it? In this context, slowing down to me means that we start to see a trend in the line, whether it's plotted on a log or a linear scale, that if it continues, it will curve around towards a peak, and then start going downwards. Yes, it has to be going downwards for the rate of growth itself to be decreasing, but that's not what we are initially interested in seeing - first you want to see signs that it's no longer shooting skywards in exponential fashion, then you want to see a peak appear and then of course you want to see a decline.
However...in any case when I looked more closely at those graphs last night, I realised that I don't think they are plotting absolute numbers of omicron cases, I think they are plotting proportion of all cases that are omicron cases, so they aren't actually showing what I initially though they were.