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How can I recover license file or other not-obvious app data from a backup made by Time Machine?

I would make the effort to pull out the SSD drive and clean it as you likely can save your data from it MacBook Pro 15" Retina Display Mid 2015 SSD Replacement. Once you have the drive out you can put it into an external case OWC - Envoy Pro ‘‘‘‘‘‘Portable, Bus-Powered USB 3.0 Enclosure For Apple Flash SSDs (June 2013-Current Mac Models). Then you can copy off your stuff to a new system.