Extract the Claude newline sequence and the session display name

app/src/lib/sessionName.ts

@@ -0,0 +1,27 @@
+import type { Project, TerminalSession } from "./types";
+
+/**
+ * What a terminal session is called on screen.
+ *
+ * The rule used to be written twice inside `MainTabs.tsx` — once in `tabLabel`
+ * for the drag ghost, once inline in `renderTab` — both local and neither
+ * exported, so the two could disagree the moment either was edited. It is here
+ * because a third caller (the note send-target picker) would have made that
+ * three.
+ *
+ * A user-set name wins and is prefixed with the project, because a custom name
+ * is usually about the work rather than the project and needs the context. The
+ * `(bash)` marker only appears on the fallback: a session someone bothered to
+ * name does not need to be told apart from its neighbours.
+ */
+export function sessionDisplayName(
+  session: TerminalSession,
+  project?: Project,
+): string {
+  const custom = project?.renamed_session_names?.[session.id];
+  if (custom) return `${session.projectName}: ${custom}`;
+  return (
+    (session.sessionName ?? session.projectName) +
+    (session.sessionType === "bash" ? " (bash)" : "")
+  );
+}