I think for all of the API endpoints, the "/api" always needs to come right after the base URL of the repository:
https://dataverse.harvard.edu/api/search?q=*
The "type" and "subtree" parameters can help narrow down the results to the items that are datasets (type=dataset) in the UCLA collection and any sub-collections (subtree=ssda_ucla):
Another option is using the
"Dataverse contents" endpoint, especially if you don't want or need the DOIs of any datasets within the sub-collection of that ssda_ucla collection:
Hope that helps! It's really interesting to think of the motivation for having the Search API, and perhaps all of the APIs, work the way you tried them (not sure if that's technically possible).