I agree with you in most contexts, but "illegal activity (in the country of service)" is a tough one in the context of an invasion, a territorial dispute, or international espionage.

Before the current war, Hamas was the governing authority in Gaza, despite the Palestinian Authority being the internationally recognized one. Regardless, whether the surveillance was legal under Israeli law doesn't seem like the correct standard.

I think that if Azure offers their service in Israel it has to comply with Israeli law; I don’t see why that would not govern in this case.

If Azure were providing service to the US Government then that service would be governed by US law even if the employees using the service traveled abroad; the only exception would be if service was initiated by an employee in another country under the terms for the service provider in that country, but even then likely government has contracts with the provider that would shift jurisdiction back to the US.