This may very well be true, but I'm having trouble believing anything, from anyone, about the conflict. There is so much propaganda around the subject, that unless you are personally connected to an official source, I believe you can't know with any reasonable certainty. The primary source for this story appears to be public Google Trends data.
This presentation is interesting because it is a data presentation that is large, direct, and open: Of Russian IPs using a Google, search terms associated with leaving are going up, even pre-war. Your own research can now be on alternative hypotheses like maybe Google became that much more popular in the last few months in spikey per-keyword patterns, or that the Russian population using Google is big (some X%) but has opposite beliefs of all non-Google users. For both, you can check against something like Yandex, which has a similar feature.