Thanks for your reply!!
I have tried that and the STLINKV2.1 on my working Nucleo Board does not find the STM32 target (meaning the STLINKV3 of the the failing board).
Let me explain how I understand this works and maybe there is something fundamental I am missing.
I have a pin header on the CN2 connector of the Nucleo-WL55JC1(failing board). I have these pins SWDIO, SWCLK, Gnd, and 3V3_STLK connected to my other Nucleo board configured for external programming. 3V3_STLK -> VDD_TARGET, SWCLK -> SWCLK, SWDIO -> SWDIO, and Gnd-> Gnd. As far as I understand it the 3V3_STLK -> VDD_TARGET connection is used to measure what the target MCU voltage, it does not provide the power to the target MCU. So I have the failing Nucleo board plugged in to provide power to the STLINKV3 MCU.
After connecting the two boards up this way, STMCubeProgrammer finds the working STLINKV2.1 but does not find any target MCU, which should be the failing STLINKV3 MCU. Either I am still doing something wrong or more is wrong with STLINKV3 MCU. I even metered out the short jumpers I am using to connect the boards and they check out.