Summary

Bamboo does have a REST API to retrieve data where QuickFilter is configured. However, this API request will only indicate the existence of available filters, not the plans associated to them.

Suggestion

As we are able to get data from database would be helpful to get the same data from a REST API endpoint.

SELECT 
    PROJECT.PROJECT_KEY, 
    PROJECT.TITLE AS PROJECT_NAME, 
    BUILD.TITLE AS PLAN_NAME 
FROM 
    PROJECT 
JOIN 
    BUILD ON PROJECT.PROJECT_ID = BUILD.PROJECT_ID 
WHERE 
    BUILD.BUILD_TYPE NOT IN ('JOB', 'CHAIN_BRANCH') 
    AND PROJECT.PROJECT_KEY = 'your_project_key';