Does Google Takeout Delete the Dates From My Photos?
No. Google Takeout does not strip your photo dates. It puts them in a separate .json file instead of inside the photo. Here is how to put them back.
No. Takeout deletes nothing: Google puts each photo's date in a .json file next to it, and many photos come back with no date inside the file, so your computer shows the download day instead.
Google Photos keeps the date in its own database, not necessarily inside your photo. When you export, Google copies that database entry into a small .json file next to each picture. The photo itself is handed back the way it was uploaded, and for screenshots, chat images and anything you edited in Google Photos, that means it has no date inside it at all. Your computer then falls back on the only date it can see: the day you downloaded the file. So your holiday from 2014 looks like it happened this morning.
The dates are sitting right there in the .json files. They just need to be written into the photos.
That is the whole job, and it is a one-run fix. Point the app at your Takeout folder and it reads every sidecar, writes the real capture date into each photo's EXIF, and sets the file dates to match. Your first 500 photos are free, so you can see it work before you decide anything.