Currently, the largest possible Switch game card that a publisher can sell tops out at 32 gigs. The Switch can support far larger sizes, and Nintendo has plans to allow larger game cards as soon as they can perfect the process. As you well know by now, Nintendo prefers to create its own means of physical game storage in an effort to stem the tide of piracy.
Nintendo had previously promised game makers that a 64 GB card would become available to use in the middle of 2018. This would have put the Switch at a slight advantage over other consoles, who still use Blu-Ray discs that can hold a max of 50 GB of data. Now The Wall Street Journal reports that due to “technical issues,” the 64 GB Switch cards won’t be offered until 2019.
Publishers have other ways of dealing with the tight space. Sometimes only part of the game will come on a card or disc, and the other part will auto-download once you put it in. Game makers have been using this strategy on the Switch — most overtly by Capcom, who published Resident Evil Revelations on Switch with a note on the box warning that a MicroSD card was a necessity. Other times, a game will fit on a 32 GB card, but to save production costs, a publisher will purposely use a smaller size and add the rest to the download.
As for Nintendo, they always keep their games lean — Breath of the Wild and Super Mario Odyssey are both under 6 GB (quite a feat when you consider how large BotW’s world is). The moral of this story is to stock up on SD cards if you own a Switch — you’ll need ’em.