Persist Schedule filter into cross-section store on submit (TZ §4.1.8)

ScheduleFilter's handleSubmit now calls setScheduleFilter with the
submitted outbound + optional return snapshot. This completes the
cross-section wiring: OnlineBoardFilter already wrote to the store
and both start pages read getBoardFilter/getScheduleFilter for
Table-10 projection on subsystem switch.

src/features/schedule/components/ScheduleFilter.tsx

@@ -19,6 +19,7 @@ import { useDictionaries } from "@/shared/dictionaries/index.js";
 import { useScheduleCalendar } from "../hooks/useScheduleCalendar.js";
 import type { IScheduleCalendarParams } from "../types.js";
 import { buildScheduleUrl } from "../url.js";
+import { setScheduleFilter } from "@/shared/state/crossSectionNavigation.js";
 import type { ScheduleParams } from "../url.js";
 import { formatScheduleDateRangeWithCurrentWeek } from "../dateLabels.js";
 import { scheduleWindowBounds } from "@/shared/dateWindow.js";
@@ -374,6 +375,29 @@ export const ScheduleFilter: FC<ScheduleFilterProps> = ({
         params = { type: "route", outbound };
       }
       const url = buildScheduleUrl(params);
+      // TZ §4.1.8: persist Schedule filter into the cross-section
+      // store so a subsequent visit to Board/Schedule within the same
+      // session can read/project it.
+      setScheduleFilter({
+        mode: "route",
+        ...(dep ? { departure: dep } : {}),
+        ...(arr ? { arrival: arr } : {}),
+        dateFrom: outbound.dateFrom,
+        dateTo: outbound.dateTo,
+        timeFrom: outbound.timeFrom ?? "0000",
+        timeTo: outbound.timeTo ?? "2400",
+        onlyDirect: directOnly,
+        showReturn: returnFlights,
+        ...(returnFlights && params.type === "roundtrip"
+          ? {
+              returnDateFrom: params.inbound.dateFrom,
+              returnDateTo: params.inbound.dateTo,
+              returnTimeFrom: params.inbound.timeFrom ?? "0000",
+              returnTimeTo: params.inbound.timeTo ?? "2400",
+            }
+          : {}),
+        searchExecuted: true,
+      });
       // Lock submit for 30 seconds (§4.1.11 — hardcoded, not configurable)
       setSubmitLockedUntil(Date.now() + 30_000);
       setNowTs(Date.now());