Sign in with same Apple ID and password on the same network on both Mac , and in your - one titled Local which is only on my MacBook
First turn on icloud drive and check the box of desktops and documents see the articles https://support.apple.com/en-us/HT206985
https://support.apple.com/en-in/guide/mac-help/mchle5a61431/10.14/mac/10.14
And drag and drop the personal documents saved locally / might be in other locations like saved in download folder > in finder location > iCloud section > over documents see the last para of the article Work with folders and files in iCloud Drive - Apple Support
Note : you don't need to again drag and drop documents literally on desktop screen of MacBook as you mentioned - How can I set up my MacBook to only have the one desktop (iCloud) .