I was having the same difficulty, using Chrome browser on Windows 7 SP1. Device manager does not see Cascadia WebUSB FPGA, and it did not show up in the WebFPGA “Connect Device” device list.
Some experience with other non-standard USB devices (software defined radios) suggested that this might be a driver issue that could be corrected by installing the WinUSB driver for this device with Zadig (zadig.akeo.ie). When I ran zadig, after using the option to “List All Devices,” the Cascadia showed up in the devices list. I then installed WinUSB (v6.1.7600.16385) for that device. Installation completed successfully.
Now, when I run the WebFPGA IDE, the “Cascadia WebUSB FPGA Programmer” shows up in the device list, I can connect to it, and have successfully flashed the WF_blinky.v example.
The Cascadia WebUSB FPGA Programmer still does not show up anywhere in Windows 7 Device Manager.