I would recommend removing the Pico 1H that comes with your PicoCalc and installing a Pimoroni Pico Plus 2W and flashing the desired UF2 file with the BOOTSEL button on applying power via the Pico Plus 2W’s USB by first copying a new (i.e. supports RP2350) flash nuke to the USB Mass Storage device that appears, and then copying your desired target UF2 file to the second USB Mass Storage device that will appear once the flash nuke is complete.
You can get the UF2 file for the latest PicoCalc Picomite from here:
BTW, here is where you can get a flash nuke UF2 that will work on any RP2040 or RP2350 board: