feat(client): open TREK on the active trip when asked to

Settings -> General -> Startup: start on the dashboard (unchanged default)
or straight in the active trip, on a tab of your choice. Three clicks and
three loads less for someone entering expenses while actually travelling,
which is where the request came from.

The redirect sits on '/' because that is what a shortcut, a bookmark and
the installed PWA all launch (manifest start_url). /dashboard keeps
working as itself - redirecting there too would leave no way back to it.

The preference is mirrored into localStorage, the way the language and
the theme snapshot already are, so the first paint can decide without
waiting on GET /api/settings. That keeps the default launch exactly as
fast as before: only someone who asked for the trip pays for the lookup,
and if it fails or they have no trip they get the dashboard. Right after
login the store already holds the real settings, so those win there.

Login stops hardcoding /dashboard as its fallback and hands the decision
to the same place, so there is one answer to "where does TREK open".

client/src/api/client.ts

@@ -19,7 +19,7 @@ import {
   type TripAddMemberRequest, type TripTransferOwnershipRequest,
   type TripCreateGuestRequest, type TripRenameGuestRequest, type AssignmentReorderRequest,
   type PackingReorderRequest, type PackingCreateBagRequest, type TodoReorderRequest,
-  type TripCreateRequest, type TripUpdateRequest, type TripCopyRequest,
+  type TripCreateRequest, type TripUpdateRequest, type TripCopyRequest, type ActiveTripResponse,
   type DayCreateRequest, type DayUpdateRequest, type DayReorderRequest,
   type PlaceCreateRequest, type PlaceUpdateRequest,
   type ReservationCreateRequest, type ReservationUpdateRequest,
@@ -372,6 +372,9 @@ export const tripsApi = {
   list: (params?: Record<string, unknown>) => apiClient.get('/trips', { params }).then(r => r.data),
   create: (data: TripCreateRequest) => apiClient.post('/trips', data).then(r => r.data),
   get: (id: number | string) => apiClient.get(`/trips/${id}`).then(r => r.data),
+  // The startup redirect's one lookup — deliberately not list(), which would pull
+  // every trip with its counts just to read one id.
+  active: (): Promise<ActiveTripResponse> => apiClient.get('/trips/active').then(r => r.data),
   update: (id: number | string, data: TripUpdateRequest) => apiClient.put(`/trips/${id}`, data).then(r => r.data),
   delete: (id: number | string) => apiClient.delete(`/trips/${id}`).then(r => r.data),
   uploadCover: (id: number | string, formData: FormData) => postMultipart(`/trips/${id}/cover`, formData),