fix(home): one new-chat intent and a scoped login-return stash (BUG-1038)

Coming back to / from /people could show the previous rectification session
as a locked page: its title in the header, the composer stuck on
"正在打开生时校正…", and the new-chat greeting in the middle.

The state that survived between pages is the sessionStorage login-return
stash that secondary-page sidebar links write from the current ?c=:
- /people「和 TA 对话」used a second intent (?newChat=1) parsed by a
  component mounted inside Home after bootstrap, so the bootstrap new-chat
  branch never ran and the stash won.
- A stash id not in the current person's loaded list was looked up and
  landed with urlAction "keep", which assumes ?c= is already in the address
  bar. It was not, so the rectification auto-open never fired. The stash
  also ignored which person was current.
- An in-page new chat left the stash in place.

Fix: delete NewChatDeepLink / ?newChat and route「和 TA 对话」through
newChatHref(); a looked-up stash writes ?c= back (replace-selected) and is
dropped when it belongs to another person; startNewChat and
openChatBoundToProfile clear the stash. ?c= deep links, BUG-989 and BUG-705
are unchanged.

Tests: new real-lifecycle suite mounting the real Home, sidebar and people
page (10 cases: four secondary pages + mobile drawer, 和 TA 对话 for self and
another person, out-of-scope stash, same-person stash beyond the first page,
in-page new chat), plus two contract/unit tests. Six fail on origin/staging,
all pass here. Full suite 3928 / 61 failing, failure names identical to the
0ab061b9 baseline (3916 / 61).

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

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

@@ -45,7 +45,7 @@ import { composerDraftSnapshot, setComposerDraft } from "@/lib/composer-draft";
 import { sessionMatchesSubject } from "@/lib/chat-profile-picker-model";
 import { bindCurrentSubjectAccount, readCurrentSubjectId, useCurrentSubjectProfile } from "@/lib/current-subject";
 import { DailyStarlanguageBinder } from "@/components/daily-starlanguage-binder";
-import { NewChatDeepLink, SynastryDeepLink } from "@/components/people-home-links";
+import { SynastryDeepLink } from "@/components/people-home-links";
 import { StarterEntries, StarterGreeting } from "@/components/starter-home";
 import {
   GENERAL_NO_MINUTE_DAILY_FORTUNE_QUESTION,
@@ -1127,7 +1127,6 @@ export default function Home() {
           natalMinuteAvailable={natalMinuteAvailable}
           setDailyStarlanguage={setDailyStarlanguage}
         />
-        <NewChatDeepLink ready={Boolean(account && modelCatalog)} startNewChat={startNewChat} />
         <SynastryDeepLink profile={profile} draft={synastryPanel.draftSynastryQuestionFromChart} />
         <span className="sr-only" role="status" aria-live="polite" aria-atomic="true">{replyAnnouncement}</span>
         {pendingSessionDeletion ? (