feat(tickets): add tickets API client, update integrations API for paginated search, fix callers

- Create frontend/src/api/tickets.ts with ticketsApi (resources, status, create, ai-parse, priorities, search)
- Update integrationsApi.searchTickets and searchTicketsQueue return types from PSATicketSearchResult[] to TicketListResponse
- Fix TicketQueue.tsx to use results.items (append/set) and results.items.length for pagination check
- Fix TicketPickerModal.tsx to use results.items when setting search results
- Export ticketsApi from api/index.ts

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

frontend/src/api/tickets.ts

@@ -0,0 +1,48 @@
+import { apiClient } from './client'
+import type {
+  PSAResource,
+  PSATicketCreated,
+  PSATicketStatusUpdate,
+  TicketCreationPayload,
+  AiParseResponse,
+  TicketListResponse,
+  PSAPriority,
+} from '@/types/tickets'
+
+export const ticketsApi = {
+  listResources: (ticketId: number): Promise<PSAResource[]> =>
+    apiClient.get<PSAResource[]>(`/integrations/psa/tickets/${ticketId}/resources`).then(r => r.data),
+
+  addResource: (ticketId: number, memberId: number): Promise<PSAResource> =>
+    apiClient.post<PSAResource>(`/integrations/psa/tickets/${ticketId}/resources?member_id=${memberId}`).then(r => r.data),
+
+  removeResource: (ticketId: number, memberId: number): Promise<void> =>
+    apiClient.delete(`/integrations/psa/tickets/${ticketId}/resources/${memberId}`).then(() => undefined),
+
+  updateStatus: (ticketId: number, statusId: number): Promise<PSATicketStatusUpdate> =>
+    apiClient.patch<PSATicketStatusUpdate>(`/integrations/psa/tickets/${ticketId}/status?status_id=${statusId}`).then(r => r.data),
+
+  createTicket: (payload: TicketCreationPayload): Promise<PSATicketCreated> =>
+    apiClient.post<PSATicketCreated>('/integrations/psa/tickets', payload).then(r => r.data),
+
+  aiParse: (prompt: string): Promise<AiParseResponse> =>
+    apiClient.post<AiParseResponse>('/integrations/psa/tickets/ai-parse', { prompt }).then(r => r.data),
+
+  listPriorities: (): Promise<PSAPriority[]> =>
+    apiClient.get<PSAPriority[]>('/integrations/psa/priorities').then(r => r.data),
+
+  searchTickets: (params: {
+    query?: string
+    board_id?: number | null
+    status_id?: number | null
+    include_closed?: boolean
+    assigned_to_me?: boolean
+    unassigned?: boolean
+    board_ids?: string
+    priority?: string | null
+    company_id?: number | null
+    page?: number
+    page_size?: number
+  }): Promise<TicketListResponse> =>
+    apiClient.get<TicketListResponse>('/integrations/psa/tickets/search', { params }).then(r => r.data),
+}