assistant2: Add new conversation button, that also saves the current conversation (#11522)

This PR updates the new assistant with a button to start a new
conversation.

Clicking on it will reset the chat and put it into a fresh state.

The current conversation will be serialized and written to
`~/.config/zed/conversations`.

Release Notes:

- N/A

crates/assistant/src/saved_conversation.rs

@@ -106,6 +106,11 @@ impl SavedConversationMetadata {
                 .and_then(|name| name.to_str())
                 .zip(metadata)
             {
+                // This is used to filter out conversations saved by the new assistant.
+                if !re.is_match(file_name) {
+                    continue;
+                }
+
                 let title = re.replace(file_name, "");
                 conversations.push(Self {
                     title: title.into_owned(),