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/app/Http/Controllers/Api/CapacityController.php

@@ -6,10 +6,12 @@ use App\Http\Controllers\Controller;
 use App\Http\Resources\CapacityResource;
 use App\Http\Resources\RevenueResource;
 use App\Http\Resources\TeamCapacityResource;
+use App\Http\Resources\TeamMemberAvailabilityResource;
 use App\Models\TeamMember;
 use App\Services\CapacityService;
 use Illuminate\Http\JsonResponse;
 use Illuminate\Http\Request;
+use Illuminate\Validation\Rule;
 
 class CapacityController extends Controller
 {
@@ -157,4 +159,40 @@ class CapacityController extends Controller
             'member_revenues' => $memberRevenues,
         ]));
     }
+
+    /**
+     * Save Team Member Availability
+     *
+     * Persist a daily availability override and refresh cached capacity totals.
+     *
+     * @group Capacity Planning
+     *
+     * @bodyParam team_member_id string required The team member UUID.
+     * @bodyParam date string required The date for the availability override (YYYY-MM-DD).
+     * @bodyParam availability numeric required The availability value (0, 0.5, 1.0).
+     *
+     * @response 201 {
+     *   "data": {
+     *     "team_member_id": "550e8400-e29b-41d4-a716-446655440000",
+     *     "date": "2026-02-03",
+     *     "availability": 0.5
+     *   }
+     * }
+     */
+    public function saveAvailability(Request $request): JsonResponse
+    {
+        $data = $request->validate([
+            'team_member_id' => 'required|exists:team_members,id',
+            'date' => 'required|date_format:Y-m-d',
+            'availability' => ['required', 'numeric', Rule::in([0, 0.5, 1])],
+        ]);
+
+        $entry = $this->capacityService->upsertTeamMemberAvailability(
+            $data['team_member_id'],
+            $data['date'],
+            (float) $data['availability']
+        );
+
+        return $this->wrapResource(new TeamMemberAvailabilityResource($entry), 201);
+    }
 }

backend/app/Http/Resources/TeamMemberAvailabilityResource.php

@@ -0,0 +1,20 @@
+<?php
+
+namespace App\Http\Resources;
+
+use App\Models\TeamMemberAvailability;
+
+class TeamMemberAvailabilityResource extends BaseResource
+{
+    public function toArray($request): array
+    {
+        /** @var TeamMemberAvailability $availability */
+        $availability = $this->resource;
+
+        return [
+            'team_member_id' => $availability->team_member_id,
+            'date' => $availability->date?->toDateString(),
+            'availability' => (float) $availability->availability,
+        ];
+    }
+}

backend/app/Services/CapacityService.php

@@ -273,6 +273,21 @@ class CapacityService
             ->mapWithKeys(fn (TeamMemberAvailability $entry) => [$entry->date->toDateString() => (float) $entry->availability]);
     }
 
+    public function upsertTeamMemberAvailability(string $teamMemberId, string $date, float $availability): TeamMemberAvailability
+    {
+        $entry = TeamMemberAvailability::updateOrCreate(
+            ['team_member_id' => $teamMemberId, 'date' => $date],
+            ['availability' => $availability]
+        );
+
+        $month = Carbon::createFromFormat('Y-m-d', $date)->format('Y-m');
+
+        $this->forgetCapacityCacheForTeamMember($teamMemberId, [$month]);
+        $this->forgetCapacityCacheForMonth($month);
+
+        return $entry;
+    }
+
     /**
      * Create a CarbonPeriod for the given month.
      */