Barry is quite correct, upload/download bandwidth has very little to do with connection establishment and stability when you consider that a chat connection is literally just a few KB/s, if that.
You could have the fastest connection in the world, but if there is a tiny amount of packet loss that can still cause a connection to drop.
No, it’s not indicative of a Twitch issue when the entirety of Twitch is not having the issue you are describing.
You also fail to understand that you can’t just compare stream performance to chat like that. You could be having momentary drops on the stream too, but guess what, that’s what the buffer is for, to let the video continue playing without interruption despite such issues as long as they are minimal.
From how you’ve described your issue so far, it sounds like either an issue with your browser, or an issue with your internet connection.