It is possible to do a search in several pdf text documents and later extract the selected text to a new file automatically
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You may indexing technique to search multiple pdfs in one go: Scheduled index updates in Acrobat DC | Adobe Content Corner
For extraction, you might have to leverage programming skills as there is no inbuilt feature for text extraction.
Also, you may check this: Adobe - Acrobat : For Windows : PDF iFilter 64 11.0.01
Let us know if that helps.
You can use the Advanced Search command to perform a search on multiple files. The results can then be exported to a CSV file.