Add a ‘Scroll to Bottom’ button in WebUI chat for long outputs

[tetrahedronix]

Feature Description

When the generated output is long and the user scrolls up to read previous messages, there is no quick way to return to the latest message in the chat view.
It would be very helpful to have a “scroll to bottom” button (for example, a downward arrow ↓ icon) that appears when the user is not at the bottom of the chat.
Clicking this button would automatically scroll the chat to the most recent message generated by the model.

Motivation

Improves usability and navigation, especially when dealing with long outputs or conversations. This is a common UX feature in chat applications and would make the WebUI more comfortable to use.

Possible Implementation

Add a floating button (bottom center or bottom right) that becomes visible when the user scrolls away from the bottom.
On click, it smoothly scrolls to the latest message.