feat(chatelet): pick check-in/check-out with the shared DatePicker

Replace the two native <input type="date"> fields on the room detail
page with the base DatePicker (Popover + shadcn Calendar), the same
component the events editor uses. Check-in is floored at today and
check-out at the morning after check-in; moving check-in past the
current check-out clears it, and any change resets the last quote.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

src/modules/chatelet/views/ChateletDetailPage.vue

@@ -1,13 +1,14 @@
 <script setup lang="ts">
-import { onMounted, ref } from 'vue'
+import { computed, onMounted, ref, watch } from 'vue'
 import { useRoute } from 'vue-router'
 import { toast } from 'vue-sonner'
+import { addDays, format } from 'date-fns'
 import { MapPin, Users } from 'lucide-vue-next'
 import { Card, CardContent } from '@/components/ui/card'
 import { Badge } from '@/components/ui/badge'
 import { Button } from '@/components/ui/button'
-import { Input } from '@/components/ui/input'
 import { Label } from '@/components/ui/label'
+import DatePicker from '@/modules/base/components/DatePicker.vue'
 import { useChatelet } from '../composables/useChatelet'
 import type { AvailabilityResult, Room } from '../types/room'
 
@@ -21,6 +22,26 @@ const checkOut = ref('')
 const checking = ref(false)
 const result = ref<AvailabilityResult | null>(null)
 
+// Same YYYY-MM-DD wire format the DatePicker speaks; the availability
+// endpoint takes the same strings.
+const today = computed(() => format(new Date(), 'yyyy-MM-dd'))
+
+// Check-out must be at least the next morning. Bumping the floor also
+// clears a check-out that the new check-in has overtaken.
+const minCheckOut = computed(() =>
+  checkIn.value
+    ? format(addDays(new Date(checkIn.value + 'T00:00:00'), 1), 'yyyy-MM-dd')
+    : today.value,
+)
+
+watch(checkIn, () => {
+  if (checkOut.value && checkOut.value < minCheckOut.value) checkOut.value = ''
+  result.value = null
+})
+watch(checkOut, () => {
+  result.value = null
+})
+
 onMounted(async () => {
   try {
     room.value = await getRoom(route.params.id as string)
@@ -86,13 +107,18 @@ async function onCheck() {
       <Card>
         <CardContent class="p-4 space-y-3">
           <div class="grid grid-cols-2 gap-3">
-            <div class="space-y-1">
+            <div class="space-y-1 min-w-0">
-              <Label for="ci">Check-in</Label>
+              <Label>Check-in</Label>
-              <Input id="ci" type="date" v-model="checkIn" />
+              <DatePicker v-model="checkIn" :min="today" placeholder="Check-in" />
             </div>
-            <div class="space-y-1">
+            <div class="space-y-1 min-w-0">
-              <Label for="co">Check-out</Label>
+              <Label>Check-out</Label>
-              <Input id="co" type="date" v-model="checkOut" />
+              <DatePicker
+                v-model="checkOut"
+                :min="minCheckOut"
+                :disabled="!checkIn"
+                placeholder="Check-out"
+              />
             </div>
           </div>
           <Button