fix(home): split starter fine print, show hints only when actionable (BUG-1041)

TASK-starter-home-polish-20260926:
- D1 today's trend moves to a sub-line under the greeting
  (.starter-greeting-sub), read from the same dailyStarlanguage state the
  warm snapshot seeds; static sentence until ready, hidden without a minute.
- D2 the line under the pills appears only for a resumable case or a
  non-self subject; the first-run and redo sentences are removed.
- BUG-1041 entrySummaryFromResponse read snake_case keys while the
  entry-summary route returns camelCase, so every account parsed as a
  first run; the parser now reads the route's shape (snake_case still ok).
- D3 daily entry icon MoonStar, credits icon Coins; D4 boundary line kept.
- Records: CHANGELOG, DESIGN, VOICE, BUG_HISTORY, PROGRESS, testing list.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_017eEAG8HD3mm8gsKXgk8uU8

frontend/src/app/(app)/page.tsx

@@ -2,7 +2,7 @@
 
 import dynamic from "next/dynamic";
 import { loadBillingPanel } from "@/lib/billing-panel-loader";
-import { Sparkles } from "lucide-react";
+import { Coins } from "lucide-react";
 import { useEffect, useMemo, useRef, useState } from "react";
 import type { FormEvent, KeyboardEvent } from "react";
 import { AccountDialogOverlay, type AccountOverlayModel } from "@/components/account-dialog-overlay";
@@ -1210,7 +1210,7 @@ export default function Home() {
           <div className="chat-header-actions">
             <div className="chat-header-rectification" data-rectification-header-slot="" ref={setRectificationHeaderSlot} />
             <button className="credit-button" type="button" onClick={(event) => openAccountDialog("billing", { returnTarget: event.currentTarget, source: "credits" })} aria-label={account ? `余额 ${account.credits} 点，会员与充值` : accountError || "读取余额中"}>
-              <Sparkles className="credit-icon" aria-hidden="true" />
+              <Coins className="credit-icon" aria-hidden="true" />
               <span>{account ? account.credits : "—"}</span>
             </button>
           </div>
@@ -1244,7 +1244,7 @@ export default function Home() {
               ) : null}
 
               {profileComplete && presetMessageFinished && !rectificationSurfaceOpen && (
-                <StarterGreeting starterGreeting={starterGreeting} />
+                <StarterGreeting starterGreeting={starterGreeting} dailyTrend={natalMinuteAvailable ? dailyStarlanguageTrend : null} dailyTrendSettled={dailyStarlanguage.kind === "ready"} />
               )}
             </div>
           ) : sessionMessagesLoading ? (
@@ -1328,13 +1328,10 @@ export default function Home() {
           {starterHomeVisible && (
             <StarterEntries
               natalMinuteAvailable={natalMinuteAvailable}
-              dailyStarlanguage={dailyStarlanguage}
               dailyStarlanguageQuestion={dailyStarlanguageQuestion}
-              dailyStarlanguageTrend={dailyStarlanguageTrend}
               productEntrypointsDisabled={productEntrypointsDisabled}
               startDailyStarlanguageConsultation={startDailyStarlanguageConsultation}
               rectificationCardLabel={rectificationCardLabel}
-              rectificationCardAction={rectificationCardAction}
               rectificationLoading={rectificationLoading}
               rectificationMutationPending={rectificationMutationPending}
               openRectificationFromHomepage={openRectificationFromHomepage}

frontend/src/app/globals.css

@@ -2258,6 +2258,23 @@ input:not([type="radio"]):not([type="checkbox"]):not([class^="ant-"]):not([class
   text-wrap: balance;
 }
 
+/* Today's trend, one quiet line under the greeting (2026-09-26). It used to be
+   glued to the rectification hint under the pills with a middle dot. Two lines
+   at most: the trend is model-written and can run long on a phone. */
+.starter-greeting-sub {
+  display: -webkit-box;
+  max-width: 560px;
+  margin: var(--space-2) auto 0;
+  overflow: hidden;
+  color: var(--color-ink-secondary);
+  font-size: var(--type-body-sm);
+  line-height: 1.55;
+  text-wrap: pretty;
+  -webkit-box-orient: vertical;
+  -webkit-line-clamp: 2;
+  line-clamp: 2;
+}
+
 /* Entry pills, under the composer. The two product entrances keep their place
    in the product but not their weight: they were 132px cards competing with the
    input for the first look. */