I think the bigger question is why they were using microsoft products in the first place. USA has been very hostile to the ICC under trump, but its not exactly a huge shift, bush was also incredibly hostile. It seems borderline incompetent to use a microsoft cloud offering given the political situation. Not to mention given the type of work they do, seems like hosting stuff off site at all is a bad plan.
How much do you think they should spend on IT to be independent from Microsoft (serious question) ? Wikipedia mentions they employ 800 persons working in several buildings and a detention center for a budget of 141 million USD. Microsoft O365 Business Premium per person is 22 USD per month so total per year is ~200k USD (online price, I imagine they can negotiate a bit for that amount of people).
Their job is to investigate war criminal despite the usa trying to block them. Its not out of the question that nsa/cia/etc would use their ties at microsoft to try and get an advanced peek at the prosecution's case.
Yes all this is expensive. Their mission is not a cheap one. Doing it right costs money.
P.s. initially i mistead and got a laugh out of the idea of wikipedia operating a detention center.