Why is my empty folder has a 134 GB size?

The file /var/www/admin/storage/logs/0 is quite probably a sparse file. That is, it doesn't contain actual data over its entire length. There are stretches that have never been written and therefore do not occupy any space on disk. If those are read then the Linux kernel just returns a series of bytes with the value 0 which compresses very well, so zip has no problem fitting the entire 1 TB file into a 7.7 GB archive. But when unpacking the archive unzip will attempt to actually write all those zeroes to disk because it doesn't know that they weren't actually there on the old server.

You have two possible courses of action:

a) Delete the file on the old server or at least exclude it from the zip archive. It probably doesn't contain anything useful anyway. A sparse logfile is quite unusual and would normally only happen because of some malfunction, improper log rotation or the like.

b) Instead of zip, use an archive program with sparse file support, like GNU tar, which is able to recreate the sparse file on the new server.