Let's be honest: The C button is almost certainly for voice chat.
The Switch 2 has a mic on it whereas the Switch does not. Third parties have already said they will support Switch 2 more than Switch 1 (Which means Nintendo will need to have systems in place for an older user base). COD is confirmed to be coming to Switch 2. The Switch 2 has another USB C on top (which could be used for USB C headsets). Nintendo has reworked their online infrastructure and set up new servers internally for something.
The main thing is: It's not a normal game input button because it's in too uncomfortable of a position. It's not a second screenshot button because that would be the dumbest thing of all time "hey guys let's include a second screenshot button for some reason but change the emblem on it so that it doesn't match the other one." It's not a cast feature because if Nintendo had a cast feature on the Switch 2, there is absolutely zero reason why it needs to be a physical button. It would make a whole lot more sense to use an icon on the home menu or an icon in a game that supports it instead. It has to be a feature that needs to be used on the fly. What would be useful on the fly? How about opening a little menu that shows your game party, and mic settings.
Ok. Now that you can read the secret text, real ones can actually read this. The above text is a diversion for Nintendo because I know what the real use is. It's actually a second home button. This way you could go home to hit the chat and cast button on the home menu 2x as fast.