NAPS2 has the capability to use optical character recognition (OCR) to make text in scanned documents searchable, rather than simply being treated as an image.
To use OCR, you first need to download each language you want to use. When you click the OCR button for the first time, you will automatically be prompted to download languages. Otherwise you can click "Get more languages" in the OCR window.
Once you've downloaded the languages you want, simply check "Make PDFs searchable using OCR" in the OCR window. Any PDFs you create after that will use OCR to make your text searchable.
NAPS2 doesn't have a way to save OCR results directly to a text file. If you just want the text you can save as PDF, and in your PDF viewer, use Select All and Copy to copy the text and paste it wherever you want.