keyboard: Tab cycles the surface's text fields, forward-only (keyboard 3 of 4)

Plain Tab now navigates instead of being pure dead weight: the global
handler dispatches lh:kbd-cycle-fields and each composer-bearing
surface answers with its own chain, gathered from live DOM at event
time (the docks mount and unmount — refs would go stale):

- chat: reading-thinking → the active dock's field → the composer,
  visual order, wrap; Tab from anywhere else focuses the first live
  field (navigate in)
- new-session + home: the composer is the whole chain — Tab navigates
  into it

Shift+Tab is untouched (the thinking-level cycle keeps it — owner
ruling); the quiz dock's rows↔thinking Tab claim stops propagation at
document level, so a claimed Tab never reaches the dispatch — no
double act.

1427 tests, tsc, lint, build green.

components/field-cycle.ts

@@ -0,0 +1,36 @@
+"use client";
+
+import { useEffect } from "react";
+
+/**
+ * TAB CYCLES THE ACTIVE SURFACE'S TEXT FIELDS (owner, keyboard round
+ * 2026-10-06): forward-only, wrapping; Tab from outside the chain
+ * focuses the FIRST field — "navigate in". Shift+Tab is NOT ours (the
+ * global thinking-level cycle owns it — owner ruling the same round),
+ * so there is no reverse gear; the chain wraps.
+ *
+ * The event (not a prop bridge): the global Tab handler dispatches
+ * `lh:kbd-cycle-fields` and each composer-bearing surface answers with
+ * its own chain, gathered at event time from live DOM — the fields
+ * mount/unmount with the docks, so a query beats stale refs. The quiz
+ * dock's own Tab claim (rows ↔ thinking, while an option question is
+ * expanded) stops propagation at the document level, so this hook only
+ * ever hears Tab on surfaces WITHOUT an active claim — no double act.
+ */
+export function useFieldCycle(fields: () => readonly HTMLElement[]) {
+	useEffect(() => {
+		const onCycle = () => {
+			const list = fields().filter((el) => el.isConnected);
+			if (list.length === 0) return;
+			const active = document.activeElement;
+			const idx = active ? list.findIndex((el) => el === active || el.contains(active)) : -1;
+			if (idx < 0) {
+				list[0]!.focus();
+				return;
+			}
+			list[(idx + 1) % list.length]!.focus();
+		};
+		window.addEventListener("lh:kbd-cycle-fields", onCycle);
+		return () => window.removeEventListener("lh:kbd-cycle-fields", onCycle);
+	}, [fields]);
+}