fix(capacity): Fix three defects - caching, save, filters

1. Slow Team Member Dropdown - Fixed
   - Added cached team members store with 5-minute TTL
   - Dropdown now loads instantly on subsequent visits

2. Error Preventing Capacity Save - Fixed
   - Added saveAvailability API endpoint
   - Added backend service method to persist availability overrides
   - Added proper error handling and success feedback
   - Cache invalidation on save

3. Filters Not Working - Fixed
   - Fixed PTOManager to use shared selectedMemberId
   - Filters now react to team member selection

Test Results:
- Backend: 76 passed ✅
- Frontend Unit: 10 passed ✅
- E2E: 130 passed, 24 skipped ✅

Refs: openspec/changes/headroom-foundation

backend/tests/Feature/Capacity/CapacityTest.php

@@ -149,6 +149,31 @@ test('4.1.16 GET /api/capacity/revenue calculates possible revenue', function ()
     expect(round($response->json('data.possible_revenue'), 2))->toBe(round($expectedRevenue, 2));
 });
 
+test('4.1.25 POST /api/capacity/availability saves entry', function () {
+    $token = loginAsManager($this);
+    $role = Role::factory()->create();
+    $member = TeamMember::factory()->create(['role_id' => $role->id]);
+
+    $payload = [
+        'team_member_id' => $member->id,
+        'date' => '2026-02-03',
+        'availability' => 0.5,
+    ];
+
+    $response = $this->postJson('/api/capacity/availability', $payload, [
+        'Authorization' => "Bearer {$token}",
+    ]);
+
+    $response->assertStatus(201);
+    $response->assertJsonPath('data.date', '2026-02-03');
+
+    assertDatabaseHas('team_member_daily_availabilities', [
+        'team_member_id' => $member->id,
+        'date' => '2026-02-03 00:00:00',
+        'availability' => 0.5,
+    ]);
+});
+
 test('4.1.17 POST /api/holidays creates holiday', function () {
     $token = loginAsManager($this);