refactor: split chat/transport/matrix/bot/messages.rs (912) into mod + on_room_message + handle_message

The 912-line messages.rs is split:

- on_room_message.rs: incoming Matrix event dispatch (~600 lines)
- handle_message.rs: LLM turn + reply streaming (~265 lines)
- mod.rs: format_user_prompt + tests (~70 lines)

Tests stay co-located with format_user_prompt in mod.rs.

All 2636 tests pass; clippy clean.

server/src/chat/transport/matrix/bot/messages/mod.rs

@@ -0,0 +1,66 @@
+//! Matrix message handler — processes incoming room messages and dispatches commands.
+
+mod handle_message;
+mod on_room_message;
+
+pub(in crate::chat::transport::matrix::bot) use handle_message::handle_message;
+pub(in crate::chat::transport::matrix::bot) use on_room_message::on_room_message;
+
+/// sender is included so the LLM can distinguish participants.
+pub(super) fn format_user_prompt(sender: &str, message: &str) -> String {
+    format!("{sender}: {message}")
+}
+
+/// Matrix event handler for room messages. Each invocation spawns an
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    // -- format_user_prompt -------------------------------------------------
+
+    #[test]
+    fn format_user_prompt_includes_sender_and_message() {
+        let prompt = format_user_prompt("@alice:example.com", "Hello!");
+        assert_eq!(prompt, "@alice:example.com: Hello!");
+    }
+
+    #[test]
+    fn format_user_prompt_different_users() {
+        let prompt = format_user_prompt("@bob:example.com", "What's up?");
+        assert_eq!(prompt, "@bob:example.com: What's up?");
+    }
+
+    // -- OAuth login link formatting ----------------------------------------
+
+    #[test]
+    fn oauth_error_produces_login_link() {
+        let err = "OAuth session expired or credentials missing. Please log in: http://localhost:3001/oauth/authorize";
+        let url = crate::llm::oauth::extract_login_url_from_error(err);
+        assert!(url.is_some(), "should extract URL from OAuth error");
+        let msg = format!(
+            "Authentication required. [Click here to log in to Claude]({})",
+            url.unwrap()
+        );
+        assert!(msg.contains("http://localhost:3001/oauth/authorize"));
+        assert!(msg.contains("[Click here to log in to Claude]"));
+    }
+
+    #[test]
+    fn non_oauth_error_not_formatted_as_link() {
+        let err = "Some unrelated error";
+        assert!(crate::llm::oauth::extract_login_url_from_error(err).is_none());
+    }
+
+    // -- bot_name / system prompt -------------------------------------------
+
+    #[test]
+    fn bot_name_system_prompt_format() {
+        let bot_name = "Timmy";
+        let system_prompt =
+            format!("Your name is {bot_name}. Refer to yourself as {bot_name}, not Claude.");
+        assert_eq!(
+            system_prompt,
+            "Your name is Timmy. Refer to yourself as Timmy, not Claude."
+        );
+    }
+}