Well, you do have to worry about customers using old client libraries / SDKs, even if your whole backend has migrated to a new API.

Many customers don't like to upgrade unless they need to. It can be significant toil for them. So, you do see some tail traffic in the wild that comes from SDKs released years ago. For a service as big as S3, I bet they get traffic from SDKs ever longer than that.

the server has to be compatible with old clients, but new clients don't have to be compatible with old servers, which is the case here

I think you've got the contract backwards. The server can't break old clients, but new clients can break the old server since Amazon controls the old server and can ensure that all of them are fully upgraded before the client updates are published.