Hello 정락,
Thank you for reaching out to the Microsoft Community and I'll be glad to assist you today.
You cannot locate the product key in the Windows.old folder. This folder only contains files and folders from your previous Windows installation.
By default, when you sign in with your Microsoft account, the key (digital license) will be automatically detected, and you no longer need to activate the product separately.
To find the product key installed on your device, you can use the Showkey Plus app from the Microsoft store.
https://apps.microsoft.com/detail/9pkvzcprx9nv
Disclaimer: This app is a third-party application available on the Microsoft Store and is not published by Microsoft. So, check for any ads and proceed with caution.
I hope this information helps. If you have any questions, please let me know and I will be happy to help you further.
Best regards,
Gunasekar N