Tree panel: animated width toggle, no reflow flash; steady chat header

- The three panel modes were three separate fixed-width asides, so a
  mode switch jumped the whole transcript column width in one frame:
  scrollbar flash, overshoot, re-correct. Now ONE aside animates its
  width exactly like the left sidebar (reusing the sidebar-motion
  hook, so it inherits the provider's mount-gated transition), with
  a FIXED-width inner layer clipped by overflow-hidden — content
  never reflows mid-transition.
- The chat header was auto-height: the sidebar toggle (a size-9 icon
  button) renders only while the sidebar is closed, so opening it
  collapsed the row and slid the title + phase chip up. The header is
  now a constant h-10.

next-env.d.ts

@@ -1,7 +1,7 @@
 /// <reference types="next" />
 /// <reference types="next/image-types/global" />
-import "./.next/dev/types/routes.d.ts";
-import "./.next/dev/types/root-params.d.ts";
+import "./.next/types/routes.d.ts";
+import "./.next/types/root-params.d.ts";
 
 // NOTE: This file should not be edited
 // see https://nextjs.org/docs/app/api-reference/config/typescript for more information.