The uf2 images are mostly for the Pico 1. They will all have to be updated to work with the Pico 2 or 2 W. PicoMite has already been updated for the Pico 2, but not the 2 W. You can get the Pico 2 uf2 here;
Edit: Let me clarify slightly. The updated PicoMite uf2 for the Pico 2, will run on a Pico 2 W, it just does not support the wireless. For wireless support WebMite needs to be updated for the PicoCalc and that has not happened yet.