This applies to both games
Pokemon Stadium transfers are a no-go, according to the tiny text right there in the accompanying sizzle reel for the recent Nintendo 64 Switch additions.
Backing up a bit, during this week’s Nintendo Direct, Nintendo confirmed a heap of Nintendo 64 games coming to Switch Online’s Expansion Pack scheme: Pilotwings 64, Mario Party 64, Mario Party 2, Mario Party 3, Pokemon Stadium, Pokemon Stadium 2, 1080 Snowboarding, Excitebike 64, and GoldenEye 64.
Wait, Pokemon Stadium 1 and 2?! Yep! That seemingly includes the minigames, which for a lot of folks, are the real reward. Though naturally, the addition of these two into the mix did spark the discussion of transfers, which are a no-go. According to the text on the bottom of the screen during the introduction of those two re-releases: “Pokemon cannot be transferred to these games.”
Given that rental Pokemon are an underlying part of the core series and the aforementioned minigames are in play, all of the as-is functionality of the two games softens the blow. That said, the inability to bring creatures in will make the core experience that much more arduous for a lot of folks (though there are completion runs with just rentals). At one point, transferring Pokemon into the Stadium series was an amazing gimmick, but for now, it’ll be relegated to the past.
If you’re interested in part of the reasoning behind the scenes, Serebii.net webmaster Joe Merrick breaks it down in a Twitter thread. It essentially has to do with reading Transfer Pak data, and how interactivity with the 3DS in any shape or form is not a priority for Nintendo given the imminent shutdown.