The 2022 version of Pr actually does this easily. Without need of any other app.
The way I suggest using it is to make a sequence of each clip. Go to the Captions workspace, and select Transcribe from the Text panel. Then after it's done, "Create subtitles". Then from the Text panel, the three-dot menu to the far right, you can choose to create a text file from the captions.
Now you can print out that text file, reading through for the bits you want, mark your text file. Go to each clip and simply tap in the timecode and get to the bits you want.