I would use a USB connected SSD like I use for backup as probably the fastest way of doing it.
Absolutely agree (but I haven't read through the whole thread now, maybe this has already been posted in a similar way).
Either way, it will take time. In general, there is a problem with copying files, which definitely makes the speed of USB take a back seat. The transfer speed of USB 3.0 or USB 4.0 may be relatively high. But that's only half the story. The copying speed depends primarily on the processing speed of the file system on the USB hard drive and on the target system. In other words: If you copy a folder of 3GB in size but containing 30,000 tiny files to another medium, you will at best reach the speed of USB 1.0 at some point. Each file must of course also be entered in the administration directory on the target computer and this will then slow down the file transfer very quickly.
But who cares? Well, you have a new computer and want to copy the data. Attach the USB hard drive and simply push it on. It just takes as long as it takes. And then do the whole thing again...
And the variant via NAS...
Well, sending and reading data to the network drive at the same time may seem advantageous at first glance. However, the read and write processes then interfere with each other.
Ethernet cable is also a solution, but not everyone may have it at home. A fast USB disc might be more suitable. It still takes time... Does an hour more or less really matter?