I think what JLCPCB is referring to is probably the Infineon WiFi module CY43439KUBGT that you see on the PICO W.
For module like that, the components are packed and small, if moisture is trapped inside the metal shield, during reflow process, component(s) can pop and jump off the PCB, causing damage/malfunction that it would be very difficult to find out. For such kind of modules, it usually requires at least 24 hours of baking.
They are not trying to get you to pay extra? They've been professional.
Edit:
If you buy such module directly from vendor, it will shipped in seal anti-moisture package, in addition with the instructions like the one shown in the picture below.

