Whenever you see this icon in explorer, that indicates that UAC will be involved in what you are trying to do.

Here's a good write-up on UAC.
https://www.digitalcitizen.life/uac-why-you-should-never-turn-it-off/
If you want to avoid those prompts, then the process that is doing the file copy must be running elevated with "run as administrator". Explorer does not run elevated.
The easiest way to do that is to launch a command prompt with "run as administrator". Then you can run command line programs to copy the files.

"Run as" UAC prompt.

The windows title will show "Administrator", and any program that you run from this prompt will have admin rights.

Robocopy is a powerful utility for copying files. That would be your best bet.
https://lazyadmin.nl/it/robocopy-ultimate-guide/
If you frequently run into this problem, then you have a permissions issue. The question that you would need to ask yourself is: why do I have these folders locked down so that only Administrators have update access?
If you don't have any major security requirements, then just grant the Users group full control. You can do this on both the source and destination folders. Caveat: you really need to think about which folders you do that to. For example, you would NOT want to modify permissions on the root of the C: drive. Or C:\Windows. You would only want to do that on data folders that you created.

If you are unsure about what permissions are defined on subfolders, you can set the permissions to what you want on a parent folder and then push the permissions to all subfolders and files.

There are plenty of sites on the net that document how to set NTFS permissions. I recommend that you browse a few of them to get better understanding of how to manage permissions. If you then have a specific question or problem, I'll certainly try to answer it for you.
https://www.bing.com/search?q=windows%20file%20permissions%20tutorial