feat(rooms): Fix NaN online stats + Add DAARWIZZ CTA on homepage

- Fixed NaN in online stats by using nullish coalescing (?? 0)
- Added members_online, zone, room_type to /api/v1/city/rooms response
- Added DAARWIZZ chat CTA section on homepage with link to city-lobby
- Created task files for next phases:
  - TASK_PHASE_CITY_ROOMS_FINISH_v2.md
  - TASK_PHASE_AGENT_MANAGEMENT_v1.md
  - TASK_PHASE_CITIZENS_DIRECTORY_v1.md

docs/tasks/TASK_PHASE_CITIZENS_DIRECTORY_v1.md

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+# TASK_PHASE_CITIZENS_DIRECTORY_v1
+
+## Title
+TASK_PHASE_CITIZENS_DIRECTORY_v1 - Public Citizens Directory and Agent Visibility
+
+## 1. Overview
+
+Make /citizens page fully functional as public AI-citizens directory:
+
+* Show list of agents marked as public.
+* Support filters: search, district, agent type.
+* Connect Publichnyi hromadianyn mista toggle in agent Identity tab to this directory.
+
+## 2. Current State
+
+* /citizens page exists, but shows:
+  * Found citizens: 0
+  * Error: Failed to fetch citizens
+
+* Agents page /agents shows many agents (including NODE2 DAGI agents).
+
+* On agent Identity tab there is toggle:
+  * Publichnyi hromadianyn mista
+  * Rezhym vydymosti: Publichnyi / Tilky MicroDAO
+
+* Backend likely missing:
+  * Proper get_public_citizens() query.
+  * Or route /public/citizens is broken.
+
+## 3. Goals
+
+1. Make /citizens page show a list of public agents.
+2. Wire visibility controls on agent Identity tab to is_public field.
+3. Filters work:
+   * Search by name/title/tagline.
+   * District filter.
+   * Agent type filter.
+
+## 4. Backend Tasks
+
+### 4.1. Citizen model
+
+Add CitizenSummary model with fields:
+- id, slug, display_name, role, public_tagline
+- district, public_district, home_microdao_id
+- kind, node_id, avatar_url, color_hint, status
+
+### 4.2. Repo: get_public_citizens
+
+Query agents WHERE is_public = true AND deleted_at IS NULL AND is_archived = false.
+Apply filters for district, kind, and search.
+
+### 4.3. API route
+
+GET /public/citizens with optional query params: search, district, kind.
+
+### 4.4. Update agent visibility
+
+PATCH /city/agents/{agent_id}/visibility to update is_public and visibility_scope.
+
+## 5. Frontend Tasks
+
+### 5.1. Fix Citizens API call
+### 5.2. Citizens Page UI with filters
+### 5.3. Citizen Card Component
+### 5.4. Wire Identity Tab to visibility API
+
+## 6. Acceptance Criteria
+
+1. /citizens page loads without error.
+2. At least one agent with is_public=true appears in Citizens Directory.
+3. Filters work.
+4. Changing visibility on /agents/[slug] Identity tab updates /citizens.
+5. No leakage of deleted/archived agents.
+
+## 7. Districts Reference
+
+* leadership - Leadership Hall
+* system - System Control Center
+* engineering - Engineering Lab
+* marketing - Marketing Hub
+* finance - Finance Office
+* web3 - Web3 District
+* security - Security Bunker
+* vision - Vision Studio
+* rnd - R&D Laboratory
+* memory - Memory Vault
+