Azure provides shared access signatures ([1], [2], [3]) that can delegate access (read/write) to specific blobs/containers/tables/queues in an Azure Storage account using an access key generated through the REST API. Does AWS offer a similar feature?

Presigned URL in S3 is the equivalent:
https://docs.aws.amazon.com/AmazonS3/latest/dev/ShareObjectPreSignedURL.html

There are also ways to generate them with SDKs not mentioned in this documentation, you can google it.

Python for example:
https://boto3.amazonaws.com/v1/documentation/api/latest/guide/s3-presigned-urls.html