I'm wondering if it's a matter of the new Dell not throwing off enough power? That it's enough to turn the light on, but not I/O data? But is that even reasonable, that they would make a business laptop that wouldn't work with the most basic of peripherals?
It's possible.
When a device is connected to a port, the port, as per the standard, only needs to provide 100mA of current at maximum. This is not enough for any external drive, though. What happens then is that the drive negotiates for more power. According to the USB spec, a USB 2.0 host can only provide up to 500mA of current per-port.
Most external drives require more than that to spin up their drives, except for very low-power versions, mind you. So how does that work?
USB has a separate specification called the Power Delivery Specification. This tends to get supported on the vast majority of devices, and allows a device to negotiate for far more current (I think the limit is up to 2 Amps). However, support is not universal.
It could be the case that the system you have doesn't support the Power Delivery Specification.
Another possibility could be that the in-circuit semiconductor fuse for the USB port(s) causes an effective current limit of less than 500mA. For the device this could be pulling down the voltage, causing the logic board to be unable to do it's work, like a semi-conscious accountant being asked to do taxes.
From what I was able to find, a 2.5" WD Passport drive needs 600mA to function properly. so it is possible this is the case. I was able to find some other references to some laptop systems having issues with devices that require more power, and others not.
One option is a USB Y-Cable. You would be able to connect the drive to two USB Ports, and one is used for more power, allowing for 1A which should be enough for a drive like that.