I’m on mint and keyboard.frame.work works (testing the firmware on rp2040 board). What browser are you using? And is it installed as a normal system package?
Perhaps try reflashing?
Releases · FrameworkComputer/qmk_firmware · GitHub
The QMK HID commandline tool error does sound like a permission issue. Did you configure a udev rule? github.com/FrameworkComputer/qmk_hid#running-on-linux
Summary
place this file into /etc/udev/rules.d/.
Once added, run the following:
sudo udevadm control --reload-rules
sudo udevadm trigger
~edit~ If anyone else needs to apply this just to get keyboard.frame.work to connect, please post your distro.