This link says that the C3-Mini uses pin2 as SCK.
https://mischianti.org/wemos-lolin-esp32-c3-mini-v2-1-high-resolution-pinout-and-specs/
This matches the pins_arduino.h information.

For the Pico, this one has different information:
https://mischianti.org/wemos-lolin-esp32-c3-pico-high-resolution-pinout-and-specs/

Which is correct?

The second piece of information is incorrect, as is the pin definition in Arduino, where the SCK pin is set to 2. I tested it for the C3 Pico and couldn't get my sketch to work with the standard pin definition. At https://www.wemos.cc/en/latest/c3/c3_pico.html and https://www.wemos.cc/en/latest/_static/files/sch_c3_pico_v1.0.0.pdf
I then saw that SCK is set to pin 1. After setting the SCK pin to 1 in the pin definition, it worked.

I haven't tested it for the C3 mini, but in the schematic https://www.wemos.cc/en/latest/_static/files/sch_c3_mini_v2.1.0.pdf the SCK pin is set to 1, so the pin definition in Arduino (SCK = 2) is probably incorrect.
Greetings, Bernhard