Fix issues #2-#6 and #8: searchable pickers, occupancy filter, asset UX, counts

- #2 #5: Replace plain <select> location pickers in NewTask and Assets with
  SearchSelect combobox — full-text search across name and category group
- #3: Add "Unknown" checkbox on asset install date — disables the field and
  saves null instead of leaving an ambiguous blank
- #4: Add inline "Add service task" form in asset detail modal — creates a
  recurring template pre-linked to the asset without leaving the page
- #6: Fix unoccupied rooms filter — was always empty because (a) list_type
  was 'all' instead of 'staying' and (b) only checked b.site_id but NewBook
  returns booking_site_id on most account configs
- #8: Add open-task count badges to category filter chips on Summary page

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/src/lib/newbook.js

@@ -60,7 +60,7 @@ export async function fetchBookings(fromDate, toDate) {
   const res = await callApi('bookings_list', {
     period_from: `${fromDate} 00:00:00`,
     period_to:   `${toDate} 23:59:59`,
-    list_type:   'all',
+    list_type:   'staying',
   })
   return res?.data ?? []
 }

backend/src/routes/tasks.js

@@ -30,9 +30,9 @@ async function fetchOccupiedSiteIds() {
   const bookings = await fetchBookings(today, today)
   const occupied = new Set()
   for (const b of bookings) {
-    if (String(b.booking_status).toLowerCase() === 'arrived' && b.site_id != null) {
-      occupied.add(String(b.site_id))
-    }
+    // NewBook returns booking_site_id on some account configurations, site_id on others
+    const siteId = b.booking_site_id ?? b.site_id
+    if (siteId != null) occupied.add(String(siteId))
   }
   return occupied
 }