refactor(coach): consolidate launch button to inline + layout-FAB shape

Lift the mobile FAB out of <CoachLaunchButton> into a new
<LayoutCoachFab> mounted once next to <CoachLaunchProvider> in the
Insights layout. Each sub-page previously mounted <CoachLaunchButton>
which rendered BOTH the FAB and the inline pill, so a phone user
ended up with 2-3 duplicate FAB nodes in the a11y tree (collapsed
visually by fixed positioning). The inline pill stays on the per-page
action rows where copy + position matter; the FAB now paints exactly
once per Insights surface.

src/app/insights/layout.tsx

@@ -1,6 +1,7 @@
 import type { ReactNode } from "react";
 
 import { InsightsLayoutShell } from "@/components/insights/insights-layout-shell";
+import { LayoutCoachFab } from "@/components/insights/layout-coach-fab";
 import { LayoutCoachMount } from "@/components/insights/layout-coach-mount";
 import { CoachLaunchProvider } from "@/lib/insights/coach-launch-context";
 
@@ -20,11 +21,18 @@ import { CoachLaunchProvider } from "@/lib/insights/coach-launch-context";
  * strip + suggested-prompt chips. Decision F (audit MA3) drove the
  * promotion: a mobile user who navigates from `/insights` to
  * `/insights/blutdruck` keeps a one-tap path back into the Coach.
+ *
+ * v1.4.28 R3c — the mobile FAB now also lives here via
+ * `<LayoutCoachFab>` (carved out of `<CoachLaunchButton>` so each sub-
+ * page mount no longer duplicates the FAB into the a11y tree). The
+ * inline `<CoachLaunchButton>` pill stays on the per-page action rows
+ * where copy + position matter.
  */
 export default function InsightsLayout({ children }: { children: ReactNode }) {
   return (
     <CoachLaunchProvider>
       <InsightsLayoutShell>{children}</InsightsLayoutShell>
+      <LayoutCoachFab />
       <LayoutCoachMount />
     </CoachLaunchProvider>
   );

src/components/insights/coach-launch-button.tsx

@@ -8,14 +8,17 @@ import { useTranslations } from "@/lib/i18n/context";
 import { useCoachLaunch } from "@/lib/insights/coach-launch-context";
 
 /**
- * v1.4.27 R3d MB4 — Coach launch button.
+ * Inline desktop Coach launch button.
  *
- * Decision F: every routed Insights sub-page mounts this button so the
- * Coach drawer (mounted at the layout root) is always reachable. The
- * button renders as a sticky-bottom FAB on `<lg` viewports (so a phone
- * user always sees it within thumb range) and as an inline header
- * action on `lg+` (where the desktop drawer slides in from the right
- * edge and the FAB would overlap the chart legend).
+ * v1.4.28 R3c — the legacy implementation rendered BOTH a sticky FAB
+ * (visible `<lg`) and the inline pill (`lg+`) from the same component.
+ * Every sub-page that mounted `<CoachLaunchButton>` therefore painted a
+ * second FAB into the DOM, collapsing to one visible button only
+ * because of `fixed` positioning — the duplicates still landed in the
+ * a11y tree. The FAB now lives once at the layout level (see
+ * `<LayoutCoachFab>` in `src/app/insights/layout.tsx`); this component
+ * keeps only the inline `lg+` pill that sub-pages mount inside their
+ * action rows.
  *
  * The button is a thin wrapper around `useCoachLaunch()` — it only
  * renders when the context provider is mounted (so dropping the button
@@ -46,48 +49,24 @@ export function CoachLaunchButton({
 
   const accessibleLabel = label ?? t("insights.heroActionAskCoach");
 
+  // Inline header-style action on `lg+`. Hidden below `lg` because the
+  // layout-level FAB (`<LayoutCoachFab>`) covers that breakpoint —
+  // mounting both at the same time would put two affordances in front
+  // of the user.
   return (
-    <>
-      {/* Sticky FAB on `<lg` viewports — pinned to the bottom-right so
-          the user's thumb always finds it. `bottom-20` clears the
-          mobile bottom navigation; `safe-area-inset-bottom` plus the
-          existing app shell padding keep it clear of the iOS home bar.
-          Hidden on `lg+` where the inline button below takes over. */}
-      <Button
-        type="button"
-        size="lg"
-        data-slot="coach-launch-fab"
-        onClick={() => launch.askCoach(prefill ?? null)}
-        aria-label={accessibleLabel}
-        title={accessibleLabel}
-        className={cn(
-          "fixed right-4 bottom-20 z-40 h-12 rounded-full px-4 shadow-lg",
-          "from-dracula-purple to-dracula-pink bg-gradient-to-br text-white",
-          "hover:from-dracula-purple/90 hover:to-dracula-pink/90",
-          "lg:hidden",
-          className,
-        )}
-      >
-        <Sparkles className="size-4" aria-hidden="true" />
-        <span>{accessibleLabel}</span>
-      </Button>
-      {/* Inline header-style action on `lg+`. Lives in the page body so
-          it picks up the sub-page layout's spacing instead of fighting
-          a sticky header overlay. */}
-      <Button
-        type="button"
-        variant="outline"
-        size="sm"
-        data-slot="coach-launch-inline"
-        onClick={() => launch.askCoach(prefill ?? null)}
-        className={cn(
-          "hidden h-10 gap-2 self-end lg:inline-flex",
-          className,
-        )}
-      >
-        <Sparkles className="size-4" aria-hidden="true" />
-        <span>{accessibleLabel}</span>
-      </Button>
-    </>
+    <Button
+      type="button"
+      variant="outline"
+      size="sm"
+      data-slot="coach-launch-inline"
+      onClick={() => launch.askCoach(prefill ?? null)}
+      className={cn(
+        "hidden h-10 gap-2 self-end lg:inline-flex",
+        className,
+      )}
+    >
+      <Sparkles className="size-4" aria-hidden="true" />
+      <span>{accessibleLabel}</span>
+    </Button>
   );
 }

src/components/insights/layout-coach-fab.tsx

@@ -0,0 +1,51 @@
+"use client";
+
+import { Sparkles } from "lucide-react";
+
+import { Button } from "@/components/ui/button";
+import { cn } from "@/lib/utils";
+import { useTranslations } from "@/lib/i18n/context";
+import { useCoachLaunch } from "@/lib/insights/coach-launch-context";
+
+/**
+ * Layout-level mobile Coach launch FAB.
+ *
+ * v1.4.28 R3c — promoted out of `<CoachLaunchButton>` (which previously
+ * rendered both the FAB and the inline pill from a single component;
+ * each sub-page mount therefore painted a duplicate FAB into the DOM
+ * before `fixed` positioning collapsed them visually). Mounting the
+ * FAB once at the layout level keeps the affordance reachable from
+ * every routed Insights surface while leaving the a11y tree with a
+ * single button.
+ *
+ * Hidden on `lg+` viewports — desktop users reach the Coach via the
+ * inline `<CoachLaunchButton>` pill that each page mounts in its
+ * action row.
+ */
+export function LayoutCoachFab() {
+  const { t } = useTranslations();
+  const launch = useCoachLaunch();
+  if (!launch) return null;
+
+  const accessibleLabel = t("insights.heroActionAskCoach");
+
+  return (
+    <Button
+      type="button"
+      size="lg"
+      data-slot="coach-launch-fab"
+      onClick={() => launch.askCoach(null)}
+      aria-label={accessibleLabel}
+      title={accessibleLabel}
+      className={cn(
+        "fixed right-4 bottom-20 z-40 h-12 rounded-full px-4 shadow-lg",
+        "from-dracula-purple to-dracula-pink bg-gradient-to-br text-white",
+        "hover:from-dracula-purple/90 hover:to-dracula-pink/90",
+        "lg:hidden",
+      )}
+    >
+      <Sparkles className="size-4" aria-hidden="true" />
+      <span>{accessibleLabel}</span>
+    </Button>
+  );
+}