fix(roadtrip): the day view drives the road picked in the road trip

A chosen alternative or a hand-bent drive is stored as vias, and only the
road trip rail routed through them. The day route on the map, its
connectors in the day list and on the phone, and the overview of all days
asked the router for the bare stops, so they drew and measured the default
road again.

They now thread the same vias between two stops that follow each other in
the stored list, with the anchor counted the way the rail counts it, and
fold the answer back to one leg per stop pair. Only while the road trip
addon is on; avoid settings and the routing engine stay with the rail.

Refs #2580

client/src/components/Map/tripRouteGeometry.test.ts

@@ -232,4 +232,26 @@ describe('tripRouteGeometry', () => {
     const byRoad = planTripRoute({ ...moving, reservations: [] }, 'driving')
     expect(byRoad.map(d => d.day.id)).toEqual([2])
   })
+
+  it('FE-MAP-TRG-013: a road picked in the road trip bends the overview and still counts as one leg (#2580)', async () => {
+    // A lodging row hides in the plan but counts in the stored list, so the via behind
+    // the first stop of day 1 is filed at 1.
+    const hotel = buildAssignment({ day_id: 1, order_index: -1, accommodation_id: 3, place: buildPlace({ lat: 48.8, lng: 2.3 }) })
+    const storedAssignments = { ...ASSIGNMENTS, '1': [hotel, ...ASSIGNMENTS['1']] }
+    const viasByDay = { 1: [{ id: 1, day_id: 1, after_order_index: 1, sequence: 0, lat: 48.95, lng: 2.6, created_at: '' }] }
+    vi.mocked(calculateRouteWithLegs).mockImplementation(async (points) => ({
+      coordinates: points.map(p => [p.lat, p.lng] as [number, number]),
+      distance: 0, duration: 0,
+      legs: points.slice(1).map(() => leg(10000)),
+    }))
+
+    const plan = planTripRoute({ ...input, storedAssignments, viasByDay }, 'driving')
+    expect(plan[0].runs[0][0].waypoints.map(p => p.lat)).toEqual([48.86, 48.95, 48.90])
+    expect(plan[1].runs[0][0].waypoints.map(p => p.lat)).toEqual([45.76, 45.80])
+
+    const summary = await routeTrip({ ...input, storedAssignments, viasByDay }, { profile: 'driving', tripId: 7, unit: 'metric' })
+    expect(summary.days[0].segments).toHaveLength(1)
+    expect(summary.days[0].distance).toBe(20000)
+    expect(summary.days[1].distance).toBe(10000)
+  })
 })