Is it possible to automatically obtain cited-by lists?
Try OpenCitations.
Using OpenCitations' COCI (guideline for their REST API here), you should see all references to {DOI} via https://opencitations.net/index/coci/api/v1/citations/{DOI}.
Example: There are 243 works citing the paper 10.1177/03058298020310031201 (according to CrossRef: is-referenced-by: 243). Use this DOI in COCI to see all these 243 references DOI-by-DOI.