As you mentioned - even remove my Apple ID account from my old Mac laptop. Given that I setup the icloud-drive storage on my old laptop, I am concerned that removing it may affect icloud access on my new laptop. Do I have any reason to be concerned?
If you sign out apple id from old Mac laptop If you sign out of iCloud on Mac - Apple Support
After signing out of iCloud on your Mac, you can still access your iCloud documents, data, photos and videos on your other devices set up for iCloud and on iCloud.com.
If you sign in to iCloud again on your Mac, your iCloud documents and data reappear on your Mac. Photos and videos you haven’t yet downloaded from iCloud Photos also appear on your Mac.
The reason behind is desktops and documents box is turned from Mac system preferences , so all documents / files are still saved on iCloud server Use iCloud Drive to store documents on your Mac and iOS devices - Apple Support
When you set up a new Mac Set up your Mac - Apple Support the same Apple ID and its password with accounts credentials that are used in old Mac will sync all documents / files Get file, folder and disk information on Mac - Apple Support when i cloud drive is turned as on Add your Desktop and Documents files to iCloud Drive - Apple Support , so you must not be worried to loose them .
