feat(tours): show a multi-day tour's stages in the list and put each on a day

A multi-day tour in the planner's list of the trip's tours now unfolds into
its stages (MDT-02), so the stages can be seen together and fitted into the
trip without leaving the one route they are cut from.

- The fold beside a multi-day tour lists its stages in route order, each
  from stop to stop with its distance, climb, descent and moving time, read
  off the saved tour the way the planner reads them, and below them what the
  whole tour adds up to. A value no stage tells is left out, a total some
  stages do not tell is marked as at least that much and says for how many,
  and a stage whose route is not planned yet says so.
- Each stage has its own day: a pill opens the trip's days, moves the stage
  to another one or takes it off again. A stage without a day shows a dashed
  "No day" pill. A day holds a tour, or one of its stages, once, and a stage
  is on one day at most; the plan's own offline path writes it.
- A stage opens in the planner: the tour opens as any tour does and the
  stage is shown once its points are in.
- The day plan names the stage a day holds with its own figures, and the
  day's route runs to that stage's start and on from its end; the trip map
  draws that stretch only. The tour list still counts a tour once, however
  many days hold it or its stages.
- A saved change that takes a stage away (its stage end gone, the tour a day
  tour again, back to the recorded track) takes it off its day in the same
  write and tells every client; the planner says so before the save.
- REST and the assign_place_to_day tool take the stage by the key of the
  stop it starts at, with the same checks; list_tours names the stops
  between the stages and the stage each day holds.

A day assignment remembers its stage by that key (migration 046010); every
assignment made before holds the whole tour, as it did.

client/src/components/Planner/DayPlanPlaceSubline.tsx

@@ -7,6 +7,7 @@ import type { Category, Place } from '../../types';
 import { formatTime } from '../../utils/formatters';
 import { fs } from '../shared/DialogShell';
 import { TourDayRowPills } from '../Tours/TourDayRowFacts';
+import { stageNumberOf, TourStageDayPills } from '../Tours/stages/TourStageDayPills';
 import { movingTimeLabel } from '../Tours/tourFacts';
 import { formatPlannedTourDuration, plannedTotalText, type TourPlannedTimes } from '../Tours/tourPresentation';
 import { WalkProgressPill } from '../Tours/walk/WalkStations';
@@ -22,6 +23,8 @@ interface DayPlanPlaceSublineProps {
   timeFormat: string;
   /** CW-03: the row's day assignment, which a city walk's progress belongs to. */
   assignmentId?: number;
+  /** MDT-02: the stage of a multi-day tour the day holds, by its starting stop's key; absent for the whole tour. */
+  tourStageKey?: string | null;
 }
 
 function hasPlannedTimes(tourTimes: DayRowTourTimes | undefined): boolean {
@@ -71,6 +74,12 @@ function PlannedTourPills({ tourTimes }: { tourTimes: DayRowTourTimes }) {
   );
 }
 
+// The tour's own pills, or a stage's where the day holds one stage of a multi-day tour (MDT-02).
+function DayRowTourPills({ tour, stageKey }: { tour: TourListItem; stageKey?: string | null }) {
+  if (stageKey && stageNumberOf(tour, stageKey) !== null) return <TourStageDayPills tour={tour} stageKey={stageKey} />;
+  return <TourDayRowPills tour={tour} />;
+}
+
 // Description line, one line like every stop's.
 function SublineDescription({ text, isTourPlace }: { text: string; isTourPlace: boolean }) {
   return (
@@ -100,6 +109,7 @@ export function DayPlanPlaceSubline({
   isTourPlace,
   timeFormat,
   assignmentId,
+  tourStageKey,
 }: DayPlanPlaceSublineProps) {
   const { locale } = useTranslation();
   const dayRowTour = tourTimes?.tour;
@@ -115,7 +125,7 @@ export function DayPlanPlaceSubline({
           {place.end_time ? ` – ${formatTime(place.end_time, locale, timeFormat)}` : ''}
         </TimePill>
       )}
-      {dayRowTour ? <TourDayRowPills tour={dayRowTour} /> : tourTimes && <PlannedTourPills tourTimes={tourTimes} />}
+      {dayRowTour ? <DayRowTourPills tour={dayRowTour} stageKey={tourStageKey} /> : tourTimes && <PlannedTourPills tourTimes={tourTimes} />}
       {dayRowTour && <WalkProgressPill tour={dayRowTour} assignmentId={assignmentId} />}
       {description && <SublineDescription text={description} isTourPlace={isTourPlace} />}
     </div>

client/src/components/Planner/DayPlanSidebar.tsx

@@ -69,7 +69,7 @@ import { RouteConnector, HotelRouteConnector } from './DayPlanSidebarRouteConnec
 import { resolveLegMode } from './legMode'
 import { useLegModeActions } from './useLegModeActions'
 import { dayExportStops, fillAroundLocked } from './dayRoute'
-import { projectDayItinerary } from '../Map/dayTourProjection'
+import { projectDayItinerary, type TourStageStops } from '../Map/dayTourProjection'
 import { usePluginDaySchedule, usePluginDayTints, dayTintBackground, dayTinted, PluginDayScheduleRow, formatScheduleMinutes } from '../Plugins/PluginDaySchedule'
 import { MobileAddPlaceButton } from './DayPlanSidebarMobileAddPlaceButton'
 import { DayPlanSidebarToolbar } from './DayPlanSidebarToolbar'
@@ -94,6 +94,8 @@ export interface DayPlanSidebarProps {
   places: Place[]
   tourPlaceIds?: ReadonlySet<number>
   plannedTourDurations?: ReadonlyMap<number, TourPlannedTimes & { tour?: TourListItem }>
+  /** MDT-02: where the stages of the trip's multi-day tours run, so a day holding one routes to that stage. */
+  tourStageStops?: TourStageStops
   categories: Category[]
   assignments: AssignmentsMap
   selectedDayId: number | null
@@ -621,7 +623,7 @@ function useDayPlanSidebar(props: DayPlanSidebarProps) {
     // legs to draw. Side-effect free, so the async loop below only does OSRM I/O.
     const planDay = (dayId: number) => {
       const merged = mergedItemsMap[dayId] || []
-      const projected = new Map(projectDayItinerary(assignments[String(dayId)] || [], toursEnabled, places).map(item => [item.assignment.id, item]))
+      const projected = new Map(projectDayItinerary(assignments[String(dayId)] || [], toursEnabled, places, props.tourStageStops).map(item => [item.assignment.id, item]))
       // Each run point carries the ORIGIN assignment's per-segment travel mode
       // (#1281): the leg from this point to the next is routed with `mode` (null =
       // inherit the day default). Transport endpoints carry no mode → day default.
@@ -840,7 +842,7 @@ function useDayPlanSidebar(props: DayPlanSidebarProps) {
     // routeDayIds is memoized from the same inputs as routeDayKey below, so keying the
     // effect on the string is equivalent while staying stable across unrelated renders.
     // eslint-disable-next-line react-hooks/exhaustive-deps
-  }, [routeDayKey, routeProfile, mergedItemsMap, accommodations, days, optimizeFromAccommodation, distanceUnit, toursEnabled, places, roadtripViasByDay])
+  }, [routeDayKey, routeProfile, mergedItemsMap, accommodations, days, optimizeFromAccommodation, distanceUnit, toursEnabled, places, roadtripViasByDay, props.tourStageStops])
 
   const openAddNote = (dayId, e) => {
     e?.stopPropagation()
@@ -2030,7 +2032,7 @@ const DayPlanSidebar = React.memo(function DayPlanSidebar(props: DayPlanSidebarP
                                   </Tooltip>
                                 )}
                               </div>
-                              <DayPlanPlaceSubline place={place} cat={cat} tourTimes={tourTimes} isTourPlace={!!isTourPlace} timeFormat={timeFormat} assignmentId={assignment.id} />
+                              <DayPlanPlaceSubline place={place} cat={cat} tourTimes={tourTimes} isTourPlace={!!isTourPlace} timeFormat={timeFormat} assignmentId={assignment.id} tourStageKey={assignment.tour_stage_key} />
                               {assignment.notes && (
                                 // Day-specific note on this stop (#2163) — one muted
                                 // caption line so the timeline shows the note exists