fix(coach): deep-link the proactive nudge to its conversation

The bottom-right launcher opened a blank new chat on an unread proactive
message instead of the thread the Coach wrote. Return the owning
conversation id from the nudge-status endpoint, have the launcher open
/coach?c=<id> on the unread path, and stamp the same deep link on the push
metadata so the notification lands in the exact conversation rather than
relying on a most-recent heuristic.

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

@@ -171,20 +171,42 @@ describe("isNudgeUnread", () => {
 
   it("is false without status or without a nudge", () => {
     expect(isNudgeUnread(undefined, null)).toBe(false);
-    expect(isNudgeUnread({ nudgedAt: null, unread: false }, null)).toBe(false);
+    expect(
+      isNudgeUnread(
+        { nudgedAt: null, unread: false, conversationId: null },
+        null,
+      ),
+    ).toBe(false);
   });
 
   it("is true for a server-unread nudge the device has not seen", () => {
-    expect(isNudgeUnread({ nudgedAt, unread: true }, null)).toBe(true);
-    expect(isNudgeUnread({ nudgedAt, unread: true }, "2026-01-01")).toBe(true);
+    expect(
+      isNudgeUnread({ nudgedAt, unread: true, conversationId: "conv-1" }, null),
+    ).toBe(true);
+    expect(
+      isNudgeUnread(
+        { nudgedAt, unread: true, conversationId: "conv-1" },
+        "2026-01-01",
+      ),
+    ).toBe(true);
   });
 
   it("is false once the server counts the nudge as read", () => {
     // The user sent a Coach message after the nudge.
-    expect(isNudgeUnread({ nudgedAt, unread: false }, null)).toBe(false);
+    expect(
+      isNudgeUnread(
+        { nudgedAt, unread: false, conversationId: "conv-1" },
+        null,
+      ),
+    ).toBe(false);
   });
 
   it("is false once this device stored the matching seen stamp", () => {
-    expect(isNudgeUnread({ nudgedAt, unread: true }, nudgedAt)).toBe(false);
+    expect(
+      isNudgeUnread(
+        { nudgedAt, unread: true, conversationId: "conv-1" },
+        nudgedAt,
+      ),
+    ).toBe(false);
   });
 });

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

@@ -1,7 +1,7 @@
 "use client";
 
 import { useEffect, useRef, useState } from "react";
-import { usePathname } from "next/navigation";
+import { usePathname, useRouter } from "next/navigation";
 import { useMutation, useQuery, useQueryClient } from "@tanstack/react-query";
 import { Sparkles } from "lucide-react";
 
@@ -49,6 +49,12 @@ const NUDGE_SEEN_STORAGE_KEY = "healthlog-coach-nudge-seen";
 export interface CoachNudgeStatus {
   nudgedAt: string | null;
   unread: boolean;
+  /**
+   * v1.22 (W5) — the conversation holding the newest assistant message, so
+   * the FAB can deep-link into the proactive thread on the unread path
+   * instead of opening a blank new chat. Null when no Coach reply exists.
+   */
+  conversationId: string | null;
 }
 
 /**
@@ -70,6 +76,7 @@ export function isNudgeUnread(
 export function LayoutCoachFab() {
   const { t } = useTranslations();
   const pathname = usePathname();
+  const router = useRouter();
   const launch = useCoachLaunch();
   const flags = useFeatureFlags();
   const disableCoach = useDisableCoach();
@@ -182,6 +189,17 @@ export function LayoutCoachFab() {
     // device, not just this one. The local stamp above already hid the
     // dot for an instant paint; the mutation makes it durable.
     if (unread) markSeen.mutate();
+    // v1.22 (W5) — when the Coach has written an UNREAD proactive message,
+    // deep-link straight into that conversation (`/coach?c=<id>`) so the
+    // user lands on what the Coach said, rather than opening a blank new
+    // chat in the drawer. The full page honours `?c=` →
+    // `initialConversationId`. Fall back to the in-place drawer for the
+    // ordinary launcher case (no unread, or no conversation id yet).
+    const conversationId = status?.conversationId ?? null;
+    if (unread && conversationId) {
+      router.push(`/coach?c=${conversationId}`);
+      return;
+    }
     // v1.16.11 — open the side drawer in place (the launch context the
     // layout mount consumes) instead of navigating to the chat page;
     // the conversation arrives without losing the page underneath.