I remember it for Pokemon, but also for those Zelda games that were a pair - Oracle of Ages/Seasons? But I don’t think it let you do much, just continue a game save when you finished one of the two games.
The Oracle games didn’t actually use the link cable, they had a password system.
It had both! You could use either a link cable or a password to continue your game in the opposite title, and to bring over the rings you had from the original save. At the jeweler’s shop, the red snake was for password transfers and the blue snake was for link cable transfers!
Four Swords came with Link to the Past too. Never played it, but it’s exclusively multiplayer, as far as I know
Four Swords is the most competitive co-op game I have ever played. It’s brutally fun, but you’re going to want to punch your friends in the throat after about 30 minutes.
https://www.penny-arcade.com/comic/2004/06/11/the-gang#
This comic is an accurate description of the experience.