RUST.md, IRIS.md, CLIENT_CORE.md: record E4 done

RUST.md: E4 ticked with the screenshot path, the exact commands against
app/ui-sandbox.sh, and the streaming-duplication bug the screenshot found;
"Where things stand" moved E4 out of "in flight" into its own done bullet.
IRIS.md: transcript_ui::build_tree, the public API change transcript-ui
gained for this. CLIENT_CORE.md: client_core::config's table row and its
correspondence note.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

IRIS.md

@@ -8,6 +8,28 @@ capability that moved. Small and trivial changes do not go here.
 An entry gives the date, what changed, why, and a short before/after where
 it helps judge the change without the session that made it. Newest first.
 
+## 2026-09-05: `transcript_ui::build_tree` (RUST.md's E4)
+
+`transcript_ui::build` claimed the whole window (`ui_state.set_root(tree)`)
+as its last step, which is right for a window that *is* the transcript
+screen (the winit example, an eventual Android cdylib) and wrong for the
+desktop app, which puts a session list beside it. `build_tree` is `build`
+minus that last step: it returns `(TranscriptScreen, StrongWidget)` instead
+of just `TranscriptScreen`, and the caller decides where the tree goes —
+into `ui_state.set_root`, or into a `WidgetPtr` alongside something else
+(`iris/desktop-app`'s `rebuild_transcript`). `build` is now one line calling
+`build_tree` and doing the `set_root` itself, so existing callers are
+unaffected.
+
+```rust
+// before, and still available, for a caller that wants to *be* the window:
+let screen = transcript_ui::build(rsc, &mut ui_state, rows);
+
+// new, for a caller embedding the screen beside something else:
+let (screen, tree) = transcript_ui::build_tree(rsc, rows);
+some_widget_ptr(rsc).set(tree);
+```
+
 ## 2026-09-05: `SpanStyle`, per-range text styling (RUST.md's I5)
 
 A `TextBuffer` used to have exactly one style (`TextAttrs`: colour, size,