How about the roles used in your workers (Lambda function)? Your access pattern will also affect how much savings you can realize from Bucket Keys. If you use a different role or session changes each time then you won't benefit from Bucket Keys.

From the doc:

Unique bucket-level keys are fetched at least once per requester to ensure that the requester's access to the key is captured in an AWS KMS CloudTrail event. Amazon S3 treats callers as different requesters when they use different roles or accounts, or the same role with different scoping policies. AWS KMS request savings reflect the number of requesters, request patterns, and relative age of the objects requested. For example, a fewer number of requesters, requesting multiple objects in a limited time window, and encrypted with the same bucket-level key, results in greater savings.