The Sandisk Connect might be a solution. It's a USB flash drive that has WiFi connectivity and after some searchsearching it appears that you can transfer files over USB and WiFi. You'd still have to manually transfer the files via web browser and I have not tried this myself, so you may want to do some more research but it should solve your worry haveof constantly unplugging it to add files to it.
https://www.sandisk.com/home/mobile-device-storage/connect-wireless-stick