Gemini has something kind of like this. In a chat, click on the "..." icon next to one of Gemini's responses and select "Branch in new chat".

It creates a new chat which has the conversation up to that point and a link to the conversation you branched it from.

The UI isn't tree-like, though. It's more like Git where each branch name is just mixed in with the rest of the soup of references.

GitHub Copilot in VS Code has a similar feature to "Fork" a conversation at any point in its history.