If you're on the same network I would just use Filezilla ftp client. Download it on both devices and you can transfer whatever between them.
Are you planning on keeping the old laptop? If it's not a proprietary drive type you could probably just take it out and pop it into your new computer. Most newer laptops can support two
SSD. If they're both M.2 drives you wouldn't even need a new cable, just a screwdriver.