Offer a spelling on every list, not just the global search

Correction only helped on the global search page, and people search from the
list they are already on. Extending it turned out to be a shape question rather
than a volume one: thirty routes take a search parameter across a dozen files,
so carrying a suggestion in each of their responses is a large change today and
one more thing every future plugin author has to remember.

So the suggestion moved to ITS OWN ENDPOINT, /api/search/suggest, which any page
can call after rendering no rows. A page that has not adopted it shows nothing,
which is exactly what it showed before - nothing breaks by omission.

The plumbing lives in useListQuery, which already owned the search term, so a
list needs three lines: take `suggestion` and `reportCount` from the composable,
call reportCount(rows.length) after a fetch, and drop SearchSuggestion into the
empty state it already has. A list that never calls reportCount never offers a
suggestion.

Wired: global search, machines, printers, PCs, network devices, measuring tools,
knowledge base, vendors. NOT wired, deliberately: the type and reference lists
(machine types, PC types, VLANs, subnets, operating systems and the rest), which
are small controlled vocabularies nobody typo-searches, and USB, whose empty
state has a different shape and wants doing by hand rather than by pattern.

TRAP FOUND WHILE WIRING IT, and left commented in every page: applying a
suggestion by calling setSearch alone updates the box and the URL and does NOT
reload the list. setSearch only syncs the URL, and the watcher that would reload
is suppressed because search.value already holds the new term - the same trap
the global search page documents in performSearch. Each page calls its own load
function directly.

The composable guards a stale answer arriving after a newer search was typed,
never offers back the word that was typed, and swallows its own errors: a search
that found nothing is already the answer, and failing to improve on it is not
worth an error in front of anyone.

The route-parity gate caught the new endpoint being served without an entry in
docs/api-inventory.json, which is hand-written on purpose; added, and the spec
regenerated from it (283 paths, 418 operations). That regeneration also carries
the openapi version to 0.12.0, left over from the release.

frontend/src/views/SearchResults.vue

@@ -42,6 +42,7 @@
 
         <div v-else-if="results.length === 0" class="no-results">
           No results found for "{{ query }}"
+          <SearchSuggestion :suggestion="suggestion" @pick="applySuggestion" />
         </div>
 
         <div v-else class="results-list">
@@ -94,12 +95,14 @@
 import { ref, computed, onMounted, watch, nextTick } from 'vue'
 import { useRoute, useRouter } from 'vue-router'
 import { searchApi, knowledgebaseApi } from '../api'
+import SearchSuggestion from '../components/SearchSuggestion.vue'
 
 const route = useRoute()
 const router = useRouter()
 
 const loading = ref(false)
 const results = ref([])
+const suggestion = ref(null)
 const query = ref('')
 const searchInput = ref('')
 const activeFilter = ref('all')
@@ -175,6 +178,7 @@ const filteredResults = computed(() => {
 async function search(q) {
   if (!q || q.length < 2) {
     results.value = []
+    suggestion.value = null
     return
   }
 
@@ -184,6 +188,10 @@ async function search(q) {
   try {
     const response = await searchApi.search(q)
     const data = response.data.data
+    // The global endpoint carries the suggestion with the results, so no second
+    // call is needed here. A list page that has no such key uses the
+    // useSearchSuggestion composable against /search/suggest instead.
+    suggestion.value = data?.suggestion || null
 
     // Handle ServiceNOW redirect
     if (data?.redirect?.type === 'servicenow') {
@@ -212,6 +220,14 @@ async function search(q) {
   }
 }
 
+// Take the offered spelling: put it in the box and search it, so the person
+// sees what was searched rather than results for a word they did not type.
+function applySuggestion(word) {
+  searchInput.value = word
+  suggestion.value = null
+  performSearch()
+}
+
 function performSearch() {
   const term = searchInput.value.trim()
   if (!term) return