I'm not sure about how the pico 8 version was included in the commercial celeste release. I thought I remember hearing that they just ported it to whatever engine they built the commercial game in, but I can't find a source for that now.
If you're interested though, I've started porting PicoLove (a Pico 8 player for Love2d) to LovePotion (TurtleP's Love2d port for Switch), and celeste classic is playable on it as of right now. Haven't made a proper release yet though, and there are plenty of incompatibilities with other carts.
The repo is on Github if you search for "picolovepotion". Unfortunately, I can't post a link because I'm a brand new member.