and the government would have to explain precisely why they decided to ban all Google services over a song about freedom.

They wouldn't explain shit. This is an authoritarian government we're talking about; they have near total control of what information gets to their populace.

More likely they'd just accuse Google of supporting terrorism, and make a show of raiding their offices and jailing their local executives.

I don’t think the people in charge would last long if that happened, considering how integral Google’s services are to many people’s lives.

This is China we're talking about. Chinese equivalents to nearly every big tech service are more than present and accounted for, even often preferred by the local populace.