It's almost certainly not the case that Gmail uses Cloud Spanner rather than Internal Spanner. I don't think Cloud Spanner (or most of Google's cloud products) have the featureset required to support loads like Gmail (both in terms of technical capability, and security/privacy features).
When I worked at Google I tried to get more services to migrate to the cloud but the internal environment that was built up over 25 years is much better at supporting billion+ users with private data.
And yet, if they do, that's probably one of the best sales pitches they could have - dogfooding. After all, isn't that also how AWS started, just reselling the services and servers they already use themselves?
It doesn't make much sense to have a 'better' version of a product you sell but keep it internal.
Yet Amazon Retail still don't use DynamoDb for the critical workloads. They still rely on an internal version of DynamoDb (Sable) which is optimized for Retail workload.
When I worked at Google I tried to get more services to migrate to the cloud but the internal environment that was built up over 25 years is much better at supporting billion+ users with private data.