The Bandai WonderSwan was the final contribution of legendary designer Gunpei Yokoi, who had previously worked at Nintendo on its Game & Watch and Game Boy ranges. Released exclusively in Japan in 1999, it offered a low-cost and highly portable alternative to Nintendo's products, but the fact that it didn't come with a built-in 3.5mm headphone jack was an early annoyance.
Part of this will have been down to Bandai's desire to create as small a unit as possible, but it also allowed the company to gain additional revenue from an accessory which allowed 3.5mm headphones to be plugged in (Nintendo performed a similar trick with the Game Boy Advance SP a few years later).
Bandai produced its own adapter, but Sammy made one, too—and both are now quite expensive on the secondary market; you can expect to pay at least $100 for an unboxed variant.
Thankfully, the adapter has been cloned and is now available for more reasonable prices:
Given that this is on Ali Express, it's fair to assume this particular model is based on zwenergy's open-source 'wsheadphone' project, which appeared a few years back.
There are other options, too, but finding them is becoming almost as tricky as tracking down an official adapter; Flash Masta's WonderBeat 9480 is currently out of stock, as is Ice System's WonderPhone.