Do I Need to Keep the Google Takeout Zip Files?
Keep them until your fixed library is checked and backed up. Here is what to verify before deleting anything.
Keep them until you have a fixed library you have actually looked at, and a backup of it.
The zips are your only copy until the export is unpacked, processed and verified. Deleting them early is how people end up running Takeout twice. Once your photos carry their own dates and locations, and that folder is backed up somewhere other than the same disk, the zips are just duplicates and you can clear the space.
Do the fixing first, because it is the step that turns the zips into something worth keeping. The app reads your export without altering it and writes a corrected library into a new folder, so the original stays untouched the whole time. Check a few photos you remember, back the result up, then delete. The first 500 photos are free.