Having a Discord would kind of make the forums useless. The point of the forums is to add a classic touch to the Tamagotchi experience, and having a non-staff member host a Tama-Talk Discord would make it hard for them to police bad behavior. We also have many people from all walks of life here, both age, and regional heritages. Without a definitive set rules, a Discord server would devolve into chaos. I don't personally feel like a Discord server suits Tama-Talk as a whole, and would lead to a lot of bad things.
TamaTalk used to have a live chatroom years ago. Unfortunately it only caused more issues than it was worth and was shutdown.
Non-zero chance it could return some day, but I wouldn't count on it. I think it was more of a relic of its time as live chats weren't as common as they are now with the ease of use that Discord provides.