fix(home): stop silent rectification open after login (BUG-599)

Bare `/` was treating the latest history session as active, so a returning account could auto-open a failed rectification Case and left-align the starter home.

Co-authored-by: Cursor <cursoragent@cursor.com>

frontend/src/lib/home-bootstrap.ts

@@ -8,8 +8,62 @@
  * settled, or when the prepare budget runs out — never with a spinner inside.
  */
 
+import { parseSessionUrlQuery } from "./chat-session-url.ts";
+
 export type BootstrapPhase = "account" | "prepare";
 
+export type LandingSession = Readonly<{
+  id: string;
+  sessionType: string;
+  messages: readonly unknown[];
+}>;
+
+export type LandingUrlAction = "keep" | "replace-selected" | "replace-clear" | "none";
+
+/**
+ * A rectification Case is opened only when the address bar names that session
+ * (`?c=`), including refresh and a login return that restored the URL. Bare `/`
+ * after login must not open the latest history item in the background.
+ */
+export function shouldAutoOpenRectificationSession(input: {
+  readonly sessionType: string | undefined;
+  readonly sessionId: string | undefined;
+  readonly search: string;
+}): boolean {
+  if (input.sessionType !== "birth_time_rectification" || !input.sessionId) return false;
+  return parseSessionUrlQuery(input.search).sessionId === input.sessionId;
+}
+
+/**
+ * Default `/` landing prefers an empty consultation so the starter home can
+ * center. Deep links and login-return URLs keep the requested session.
+ */
+export function resolveStarterHomeLandingSessionId(
+  sessions: readonly LandingSession[],
+  selectedId: string,
+  urlAction: LandingUrlAction,
+): string {
+  if (urlAction === "keep" || urlAction === "replace-selected") return selectedId;
+  const selected = sessions.find((session) => session.id === selectedId);
+  if (selected?.sessionType !== "birth_time_rectification") return selectedId;
+  const emptyConsultation = sessions.find(
+    (session) => session.sessionType === "consultation" && session.messages.length === 0,
+  );
+  if (emptyConsultation) return emptyConsultation.id;
+  const anyConsultation = sessions.find((session) => session.sessionType === "consultation");
+  return anyConsultation?.id ?? selectedId;
+}
+
+export function starterHomeLandingNeedsConsultation(
+  sessions: readonly LandingSession[],
+  landingId: string,
+  urlAction: LandingUrlAction,
+): boolean {
+  if (urlAction === "keep" || urlAction === "replace-selected") return false;
+  const landing = sessions.find((session) => session.id === landingId);
+  return !landing || landing.sessionType === "birth_time_rectification";
+}
+
 export const BOOTSTRAP_PREPARE_TIMEOUT_MS = 4000;
 export const SESSION_PREFETCH_COUNT = 5;
 
@@ -19,7 +73,7 @@ export type BootstrapPrepareState = Readonly<{
   dailyStarlanguageApplicable: boolean;
   dailyStarlanguageSettled: boolean;
   entrySummarySettled: boolean;
-  /** The selected session is a rectification session: its Case must be open and hydrated before the reveal. */
+  /** A URL-named rectification session must be opened and hydrated before reveal. */
   rectificationApplicable?: boolean;
   rectificationSettled?: boolean;
 }>;