How to copy and paste file with the "Remote Desktop" app?

I've tested this myself and it doesn't work here either.

According to Microsoft here, it's not possible. You can copy-paste text between sessions, but not files. Their proposed solution is using the old application, Microsoft Remote Desktop Connection.

As already pointed out, this functionality is not currently available in the 'Universal App' - this is, apparently, largely down to the Sandbox nature of Windows Universal Apps.

You can however C&P plain text - just not files & folders.

There is a full, official, comparison between the apps available here

You can use administrative share to access remote drive. From run menu 'Win key + R' enter \\<ComputerName>\<DiskVolumeName>$ where as “<ComputerName>” put the name of the computer with the Admin Shares enabled on it (e.g. “Computer01”) and as “<DiskVolumeName>” put the name of the volume that you want to access, (e.g. “C$” = Disk Volume C:\ , “D$” = Disk Volume D:\, etc.)

https://www.wintips.org/how-to-enable-admin-shares-windows-7/