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/hooks/use-session-management.ts

@@ -8,6 +8,7 @@ import { writeChatSession } from "@/lib/chat-session-write-contract";
 import {
   SESSION_LOOKUP_FAILED_NOTICE,
   SESSION_MISSING_NOTICE,
+  clearLoginSessionReturn,
   parseSessionUrlQuery,
   writeSessionUrl,
 } from "@/lib/chat-session-url";
@@ -348,6 +349,9 @@ export function useSessionManagement(params: SessionManagementParams) {
     pendingCreateById.current.set(nextSession.id, {
       continuedFromSessionId: options?.continuedFromSessionId,
     });
+    // A new chat is not a place to come back to (BUG-1038): drop the stashed
+    // `?c=` a secondary-page link left, or the next bare `/` reopens it.
+    clearLoginSessionReturn();
     setSessions((current) => replaceUnsavedEmptyConsultations(current, nextSession));
     setActiveSessionId(nextSession.id);
     setDraft("");
@@ -617,6 +621,7 @@ export function useSessionManagement(params: SessionManagementParams) {
       if (isUnsavedEmptyConsultation(existing)) pendingCreateById.current.delete(existing.id);
     }
     pendingCreateById.current.set(nextSession.id, {});
+    clearLoginSessionReturn();
     setSessions((current) => replaceUnsavedEmptyConsultations(current, nextSession));
     setActiveSessionId(nextSession.id);
     setDraft("");