It only takes a few seconds in a more recent (2018) Dell laptop with Windows 11 in SSD, 4,60 GHz CPU and 16 GB RAM. Finally, the same PC and laptop both take only instans to show another LaCie HDD, 1 TB and NTFS in this case. Does it all depend on the quintuple capacity of the first HDD, maybe due to indexing time? Or would it be better to try formatting it in NTFS as well? Or something else yet?
Compare the power settings between both computers, it may be set to different polling times for usb / hard drives.
Cant hurt to check what crystal disk info says while you are at it.