When a world is created and the multiplayer option is turned on, including the Visible to Lan option, it shows as turned on. But when you actually enter your world and check the multiplayer option, it is tuned off, and only is turned on when playing with cellular data, outside that, your multiplayer game, Lan, won't work. This is for the versions begining with version 1.20 and above. Again, for Minecraft PE.

Steps to reproduce:
Create a world on 1.20.81 or any other 1.20 version
Make sure the Multiplayer and Visible to Lan is on
Create the world and enter.
Once inside, check the multiplayer setting of the world.