'Connect under reset' is an STM32 thing, nrf52840 can't really do that and the probe doesn't use hardware reset pin. Once the MCU is out of pin reset, Ctrl-AP can hold the mcu in soft reset, but that's the standard behavior.
The difference between Pico and Pi Debug Probe are those 100Ω resistors on CLK/DIO lines, so I guess it working for you means I need to try again with resistors soldered.
Thanks for verifying it works!