While I agree Microsoft is going to be a major and probably the biggest competitor to Stadia, I don't think number or size of data centers makes any difference here. Microsoft has traditionally not been a "cloud" company while as Google has lived it's entire life as one. Google definitely has an advantage here given it's technically their turf. Not saying MS are incapable of delivering cloud workloads but Google definitely is considered the better of the two when it coming to cloud infrastructure and talent. This might be changing now rapidly though.
What are you talking about? Microsoft has Azure and before they had that, they had numerous Internet scale services like hotmail. Microsoft has vast experience with building and running internet scale applications. Just like Google has.
It's one thing building Azure in response to AWS and GCP and another thing innovating to support something like Google search for decades and then using the same knowledge and tech to build other cloud services. Of course Microsoft is totally capable of delivery cloud workloads but they can still be considered the underdog here when it comes to Google vs MS