limitbreak I don’t know where you read that chkdsk can do data recovery, but just to be clear, that’s not what it does. It checks your drive for errors and tries to fix file system issues, but it won’t help you recover deleted file from the hard disk.
As for built-in options in Windows 11 (or any older version) there really aren’t any that will help much here. If you already checked the Recycle Bin (you did right?) and your files aren’t there, you’ll need third-party data recovery software.
Good thing here is that since you had the same files on both your internal and external drives, you’ve doubled your chances. If one drive doesn’t have recoverable data, the other still might.
Honestly I’d suggest downloading something like Disk Drill. It’s super simple to use, works great, and has a free version with a data cap enough to get you started. I’ve personally used it a ton of times andalways had good results. Basically you just launch it, select your hard drive (or external drive) from the list, hit the Search for lost data button, and wait. That’s it. It’ll show you recoverable files after the scan.