Hi @Alice_Yang
I think I might have removed the P2 header before powering off, or not unmounted correctly. Anyways, today I have been able to flash the new debugger firmware to the device and, after removing P2 and power cycling, it is recognised by the PC. I am now back to the situation at the start of my post: "Cannot provide power to DAP bus" when trying to flash or mass erase.
I am using Linux but also tried this on a Windows machine to see how it shows in the device manager and noticed some interesting things. First, the device (after being flashed with new debugger firmware) does not appear in the device manager in the same way as your screenshot. Rather than showing "NXP LPC11Uxx VCOM" it just shows "USB Serial Device". I installed the windows driver for the board which was downloaded as part of the same .zip file as firmware.bin. I also installed mcuexpresso on the machine and installed the relevant SDK. After this, I restarted the Windows machine and the device still shows as "USB Serial Device". I know this is the correct device since it disappears/reappears as I unplug and replug the device.
Next, I tried to flash some example code as well as performing a mass erase from mcuexpresso on Windows. This produces the same result as on Linux: "Cannot provide power to DAP bus" but gives a little more context. After clicking on the gui flash button, it searches for debug probes and finds my device. Then it brings up a dialog that allows me to select between performing an erase or flashing some firmware I have built. After this, I get a new dialog called "SWD Configuration" which shows "0 available SWD Devices detected. Connect a device and try again". I then get the usual "Cannot provide power to DAP bus" error.
I am not sure why the "SWD Configuration" dialog only appear on Windows. I have checked the SWD header pins again and they are definitely all correctly placed to enable SWD. I have also performed another continuity test with a multimeter and found no issues. It seems that there is still something wrong.
I was also able to attach a logic probe to the SWCLK, SWDIO and NFC_RESET pins as I attempt to perform a mass erase from MCUexpresso

From top to bottom: SWDIO, SWCLK, RFC_RESET
I don't know enough about SWD to determine if there is an issue here