Gmail accounts will sometimes be automatically "hospitalized" -- assigned more than the usual amount of resources because for some reason they are chronically behind or growing without bound -- or "jailed" -- moved into isolation along with other bozo accounts, to keep from disturbing normal people's accounts. Not a legend.

The data has to be sharded somehow, though. You might not be hitting the same exact machine, especially for the frontend, but your data isn't just magically everywhere in "the cloud".

Not the same machines, but different groups or machines (pools, shards, farms, whatever). They'll certainly be able to move you around to balance the pools, or to decomission pools, or to put you in a pool with primary data closer to where you usually access from etc. Grouping by behavior makes sense too --- separating heavy and light users makes a lot of sense, you can serve a lot more light users from one pool, and the heavy users won't impact their service.

It isn't about the compute. This is about the databases. I don't see it as stretch that google is using a sharding strategy for their datastores.

That's not the "cattle vs. pet" as I understand it. The servers are identical, i.e. cattle. This is just a case of sticky sessions. It's a common pattern to help latency and keep resource usage down.