I hope so! Here’s the company that made the 3DS, Wii U and Switch browsers (the browser is called NetFront): https://www.access-company.com/en/
Presumably Nintendo has a good partnership with them and would likely use them again in the future. I’m assuming it costs extra to make it into a full browser app though.
Another option would be if another browser maker like Firefox tried to put one on the eShop. Seems unlikely buuut maybe it could happen.