You should be able to get WebMite in the same place you get PicoMite; for reference:
It’s just the build of PicoMite to support the Pico 1W and Pico 2W’s CYW43439 radio chip.
More directly, look in:
In there there will be http://raspi1.mypi.co/download/picocalc_v6.02.00a_final_pico_w.uf2 and http://raspi1.mypi.co/download/picocalc_v6.02.00a_final_pico2_w.uf2.