Got the error:
Running probe-run --chip RP2040 target/thumbv6m-none-eabi/debug/rp2040-project-template
Error: Failed to get information for AP ApAddress { dp: Multidrop(1002927), ap: 0 }
Total shot in the dark:
I had the weirdest troubles with debugging/programming a nrf52840. Sometimes everything worked, sometimes nothing worked. Sometimes I could flash it.
The problems where caused by a faulty gnd connection. Took me way too many hours.
If you have a voltmeter check every connection from the board to the debug probe. If you don't have one it might be time changing this (was the only way I found the faulty gnd).