Can I specify related data by slug when adding/updating content via API?

Yes, it is possible. The selection of related information for content corresponds to requests where module_id is specified with a slug.
Please send the request in the following format.

• Same format as the response for GET

"ext_1": {
  "module_id": "slug",
  "module_type": "topics"
}

• Shortened notation

"ext_1": "slug"