I am attempting to export a list of URLS all Facebook groups and pages relevant to a search query.
At present, if I search the term ("parents") in the search bar on Facebook, the drop down list is populated, but I cannot find a way to capture these links, and to do so at a large scale (given that there are thousands of groups/pages which include the term "parents")
You can't do that and should not do that. See also the Automated Data Collection Terms. It's not allowed by Facebook.