I have a Pico and tested on my machine right now. Works as expected. My config.
[mcu pico]
serial: /dev/serial/by-id/usb-Klipper_rp2040_E6605481DB509336-if00
[adxl345]
spi_bus: spi0a
cs_pin: pico:gpio1
[resonance_tester]
accel_chip: adxl345
probe_points:
125,125,20
You have the wrong CS pin in what you just posted
[adxl345]
cs_pin = rpi:None
spi_bus = spi0a