Welcome to the Airtable community!
There are a few ways of going about this. One way is to create a new rollup field for the value in question and include manual beginning/ending delimiters around each value.
For example, have the rollup produce results like this:
Then you can search on the rollup field for the value surrounded by the delimiters.
By the way, this is a community forum, and most of the people who answer questions here are volunteering their time and knowledge. Your question may have gone unanswered because many members of the forum are not familiar with using the rest API and simply didn’t know how to answer.