Why your old cords don't work:
Your Surface Pro 6 and 9 both charge via the round magnetic Surface Connect port. The newest Surface Pro dropped the traditional Surface Connect charging port entirely and charges only through USB-C. So it's not that your old cords are broken — they physically can't connect to the new machine at all. This is a change Microsoft made with the redesigned Pro line.
Why the cord is short with "no plug":
Recent Surface Pro/Laptop boxes have been shifting toward including just a USB-C cable, part of what's called the "unbundling" of power supplies from new device boxes as Microsoft pushes people toward the universal USB-C standard. If you didn't get a wall adapter, you may be trying to charge off a laptop port, low-power hub, or a random USB-A charger — which brings us to the slow charging.
Why it's charging all night:
This is almost certainly a wattage problem. Microsoft's own guidance is direct: if you connect a lower-wattage charger, or a USB-A charger with a USB-A-to-USB-C cable, your device may charge slowly or not at all, and it won't use Fast Charging. For fast charging, most recent 13-inch Surface Pro models need at least 39W or 60W, with 60W recommended for fast charging. If you're plugging into a 15–20W phone charger or a USB-A port, that's exactly the "takes all night" symptom.
USB-C and Fast Charging for Surface
Check the wattage of whatever charger you're using.
If it's under 60W, that's your culprit — grab a proper 60–65W+ USB-C PD charger.
Plug directly into the Surface's USB-C port, not through a hub or dock, since not all USB-C hubs pass through full charging, and Microsoft recommends plugging directly into the device.