Some extra information:
https://github.com/aws/aws-cdk/blob/main/packages/%40aws-cdk/aws-kms/lib/private/perms.ts should get kms:Sign and kms:Verify

https://github.com/aws/aws-cdk/blob/main/packages/%40aws-cdk/aws-kms/lib/key.ts#L14-L63 functions should be implemented here I think

Sign: https://docs.aws.amazon.com/kms/latest/APIReference/API_Sign.html
Verify: https://docs.aws.amazon.com/kms/latest/APIReference/API_Verify.html
Other KMS permissions: https://docs.aws.amazon.com/kms/latest/developerguide/kms-api-permissions-reference.html

Thanks for the request and the links to documentation @jonasclaes, I see why this would be valuable to have 🙂

You can work around this by adding to the policy documents you wish to modify, or at the least you would be able to use escape hatches to modify any existing policies as well if they don't meet your needs

I am marking this issue as p2, which means that we are unable to work on this immediately.

We use +1s to help prioritize our work, and are happy to revaluate this issue based on community feedback. You can reach out to the cdk.dev community on Slack to solicit support for reprioritization.

Check out our contributing guide if you're interested in contributing yourself - there's a low chance the team will be able to address this soon but we'll try to review a PR