You’ll be better off trying to get a proper network attached storage (NAS) rather than an enclosure. Either buy a pre-made one or make one out of parts. That way you can use the network speeds. Or you could get a usb3 pcie card, they are very cheap these days.

Does your “old computer” have usb3 or usb c? If not you’ll find it very slow to access all that data over usb 2