No - you put customer ID column in every table
Is there a specific term for the trade off of denormalized vs more easily query/shard/etc?
No, it's pretty much just called that. A good DBA will be able to strike the right balance between normalization and performance using their intuition and experience, which is one of the reasons they're often paid very well despite working in relatively ancient ecosystems.
I wonder if this could or should be a built-in feature in databases. It is "meta-data" meaning data about data, who owns it.