This is a follow up to my original attempt
https://github.com/zed-industries/zed/pull/30878 and to the PR that
eventually reverted parts of it because it broke stuff
https://github.com/zed-industries/zed/pull/31295. This new approach
attaches the `scroll_to_bottom` feature to the `chat` function, which is
triggered when the `Chat` action is dispatched by the "send" icon
buttons. With that, and from my testing, the thread doesn't forcefully
scroll as new messages are added, which was the regression I had
introduced.

Release Notes:

- agent: The panel nows scrolls to the bottom after submitting a new
message, allowing to see it more easily.