You’d need 10gb on the nas, switch, and computer, or the transfer speed will be equal to the slowest component between them. But whether you’d get that full performance comes down to the speed of the disk controllers on the nas. You either have to find some performance reviews of this exact nas, or cross your fingers when you test it out.
Corporate network routers do this.
Technically you could do this with an old Cisco switch and a shell script though. The script would ping a known address on the internet from your computer. When it becomes unpingable, the script telnets into the switch and shuts the interface for the current isp and no shuts the interface for the other isp. Very hacky, but it’s what I would do if I were in your situation and I’d use the old Cisco 3750 I’ve got laying around.
Buy your own cable modem. Buy your own router to connect to your cable modem, and use whatever dns servers you want. This saves money in the long run because you no longer pay for the equipment rental.