Usually everything is through subsidiaries. For tax and profit allocation purposes the way it works is that you set up subsidiaries in tax-friendly jurisdictions and then channel the profits to them through contracts between subsidiaries.

The general point is what does "moving away from US cloud services" mean, then?

Does it mean not using infrastructure actually located in the US? Or does it mean effectively boycotting US-owned companies that may be fully located, including infrastructure, in Europe?