Latitude 5580 and WD15 Dock

First off, if your company has disabled your system's USB ports, then you can't use any dock.  USB-C is treated by the system as just another USB port that happens to have a display output wired to it.  You might be able to get a display signal out of your USB-C port since that isn't USB data traffic, but you wouldn't be able to use anything else connected to the dock, including the audio and Ethernet ports, both of which are connected via USB internally within the dock.  And it's possible that even video output won't work.  It depends on whether video output over USB-C requires a negotiation with the USB-C controller (not sure about this) and exactly how the USB ports have been disabled.  If they're disabled at a BIOS level, then the port may not work at all.  If they're disabled using some application running within Windows, then it may be different.

But if that weren't a factor, the WD15 works with regular USB-C as long as the host also provides display output capabilities over USB-C, which the Latitude 5580 does.  The WD15 does not require and would not even use Thunderbolt 3 capabilities.  Dell's dock that uses (and requires) Thunderbolt 3 is the TB16.  Note however that the WD15 is available with two power supply options, namely 130W and 180W.  According to the WD15 FAQ page here, you should be able to use the 130W version, but I seem to remember a thread here where somebody found that with the 5580, they got warnings about an undersized power source when using the 130W version, and they got rid of that by ordering a 180W version instead.  Note also that your Targus dock might be operating as an undersized power source.  Not all docks that support Power Delivery offer the same amount of power, and if the system is connected to an undersized power source, it will throttle its performance as much as it can before resorting to continuing to drain the battery even while plugged in.  Check the wattage on the regular AC adapter included with the system.  You'll want to make sure the dock you use offers at least that much power over its USB-C connection, unless you intend to keep the system's own AC adapter directly connected in addition to the dock, but that's obviously much less convenient.