feat: add home page with search/unassigned tables; center login card

- Add home view as default: search by inv number, unassigned equipment
  table with auditory assignment, search results (assigned) table
- Add inv_number query param to GET /oboruds/ for backend search
- Center login card vertically and horizontally via flexbox

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

frontend/index.html

@@ -18,12 +18,13 @@
       <div class="row no-print">
         <nav class="no-print navbar navbar-expand-lg navbar-light">
           <div class="container-fluid">
-            <a class="navbar-brand" href="/app/">Главная</a>
+            <a class="navbar-brand" href="#" @click.prevent="showHome">Главная</a>
             <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbarNav" aria-controls="navbarNav" aria-expanded="false" aria-label="Toggle navigation">
               <span class="navbar-toggler-icon"></span>
             </button>
             <div class="collapse navbar-collapse" id="navbarNav">
               <ul class="navbar-nav me-auto mb-2 mb-lg-0">
+                <li class="nav-item"><a class="nav-link" href="#" @click.prevent="showHome">Главная</a></li>
                 <li class="nav-item dropdown">
                   <a class="nav-link dropdown-toggle" href="#" role="button" data-bs-toggle="dropdown" aria-expanded="false">Оборудование</a>
                   <ul class="dropdown-menu">
@@ -63,6 +64,100 @@
       </div>
 
       <div class="container-fluid px-4">
+
+      <!-- Главная страница -->
+      <div v-if="view==='home'">
+        <div class="row">
+          <div class="card col-md-6 col-10">
+            <div class="card-body">
+              <form @submit.prevent="doHomeSearch">
+                <div class="d-flex align-items-center gap-2">
+                  <input type="text" class="form-control w-auto" v-model="homeSearch" placeholder="инвентарный номер" />
+                  <button class="btn btn-primary" type="submit">Найти</button>
+                </div>
+              </form>
+            </div>
+          </div>
+        </div>
+
+        <div class="row mt-3">
+          <div class="card col-md-10 col-12">
+            <div class="card-body">
+              <h3 class="card-title">Нераспределённые</h3>
+              <div class="status" :class="{error: !!error}">{{ status }}</div>
+              <div class="table-responsive">
+                <table class="table datatable">
+                  <thead>
+                    <tr>
+                      <th scope="col">Инв. номер</th>
+                      <th scope="col">Название</th>
+                      <th scope="col">Аудитория</th>
+                    </tr>
+                  </thead>
+                  <tbody>
+                    <tr v-for="it in homeUnassigned" :key="it.id">
+                      <td>{{ it.invNumber ?? '' }}</td>
+                      <td>{{ it.nazvanie ?? '' }}</td>
+                      <td>
+                        <template v-if="canEdit">
+                          <select class="form-select form-select-sm d-inline w-auto" v-model="it.selectedAudId">
+                            <option value="">— выберите —</option>
+                            <option v-for="a in auditories" :key="a.id" :value="a.id">{{ a.audnazvanie }}</option>
+                          </select>
+                          <button class="btn btn-sm btn-primary ms-2" @click="assignToAuditory(it)">Назначить</button>
+                        </template>
+                        <template v-else>—</template>
+                      </td>
+                    </tr>
+                    <tr v-if="homeUnassigned.length === 0">
+                      <td colspan="3" class="text-muted text-center">Нераспределённого оборудования нет</td>
+                    </tr>
+                  </tbody>
+                </table>
+              </div>
+            </div>
+          </div>
+        </div>
+
+        <div class="row mt-3" v-if="homeSearchResults.length > 0">
+          <div class="card col-md-10 col-12">
+            <div class="card-body">
+              <h3 class="card-title">Распределённые</h3>
+              <div class="table-responsive">
+                <table class="table datatable">
+                  <thead>
+                    <tr>
+                      <th scope="col">Инв. номер</th>
+                      <th scope="col">Название</th>
+                      <th scope="col">Аудитория исходная</th>
+                      <th scope="col" v-if="canEdit">Аудитория переноса</th>
+                    </tr>
+                  </thead>
+                  <tbody>
+                    <tr v-for="it in homeSearchResults" :key="it.id">
+                      <td>{{ it.invNumber ?? '' }}</td>
+                      <td>{{ it.nazvanie ?? '' }}</td>
+                      <td>{{ getAuditoryName(it.aud_id) }}</td>
+                      <td v-if="canEdit">
+                        <select class="form-select form-select-sm d-inline w-auto" v-model="it.selectedAudId">
+                          <option value="">— не менять —</option>
+                          <option v-for="a in auditories" :key="a.id" :value="a.id">{{ a.audnazvanie }}</option>
+                        </select>
+                        <button class="btn btn-sm btn-outline-primary ms-2" :disabled="!it.selectedAudId" @click="assignToAuditory(it)">Перенести</button>
+                      </td>
+                    </tr>
+                  </tbody>
+                </table>
+              </div>
+            </div>
+          </div>
+        </div>
+
+        <div class="row mt-2" v-if="homeSearchDone && homeSearchResults.length === 0">
+          <div class="col-12 text-center text-muted">Ничего не найдено по запросу «{{ homeSearch }}»</div>
+        </div>
+      </div>
+
       <div v-if="view==='byAud'" class="row">
         <div class="card col-12">
           <div class="card-body">