fix(tours): clear the last lint, knip and wiring findings of the follow-up

The unused day pills go, a client-only type stops being exported, the place
form context moves out of the page hook so its view model stays the first
object it returns, the place form test helpers split the stub component
from the plain setup, and four router files are formatted.

client/src/api/skiRoute.ts

@@ -4,7 +4,5 @@ import apiClient from './client';
 /** The piste router: a ski tour's legs planned on the piste data the server keeps, held to the contract. */
 export const skiRouteApi = {
   plan: (tripId: number | string, request: SkiRouteInput, signal?: AbortSignal): Promise<SkiRouteResponse> =>
-    apiClient
-      .post(`/trips/${tripId}/ski/route`, request, { signal })
-      .then((r) => skiRouteResponseSchema.parse(r.data)),
+    apiClient.post(`/trips/${tripId}/ski/route`, request, { signal }).then((r) => skiRouteResponseSchema.parse(r.data)),
 };