A couple of points. There is no “Libre account” and LibreOffice has nothing to do with this problem. You don’t say which Operating System you are using but I will assume it is M-S Windows. Your private documents are probably stored in a folder called “My Documents” and you need to copy all the contents of that folder onto a thumb drive or other portable storage device, and then copy them to the same folder on your new computer. The store where you bought your new laptop could help with this, as a service).
Your files only show up in LibreOffice because it keeps track of where your documents are stored, as a convenience. But LibreOffice doesn’t control that storage. To access these documents for the first time on your new computer, use your Operating System’s file manager, or search for them with LibreOffice (menu File → Open).
Your e-mails are different because they are stored, literally, on someone else’s computer (“cloud”). That is why you can access them from anywhere.