feature: a minimal implementation of the appointment feature done.

frontend/src/lib/api/appointments.ts

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+import { apiClient } from './client';
+import type { AppointmentColumnProvider, AppointmentRecord } from '@/types/appointment';
+
+export interface CreateAppointmentBody {
+  patientId: string;
+  providerUserId: string;
+  startAt: string;
+  endAt: string;
+  purpose: string;
+}
+
+export const appointmentsApi = {
+  columnProviders: async (): Promise<{ success: boolean; data: AppointmentColumnProvider[] }> => {
+    const response = await apiClient.get('/appointments/column-providers');
+    return response.data;
+  },
+
+  list: async (params: { from: string; to: string }): Promise<{ success: boolean; data: AppointmentRecord[] }> => {
+    const response = await apiClient.get('/appointments', { params });
+    return response.data;
+  },
+
+  create: async (body: CreateAppointmentBody): Promise<{ success: boolean; data: AppointmentRecord }> => {
+    const response = await apiClient.post('/appointments', body);
+    return response.data;
+  },
+
+  remove: async (id: string): Promise<{ success: boolean }> => {
+    const response = await apiClient.delete(`/appointments/${id}`);
+    return response.data;
+  },
+};

frontend/src/lib/appointmentTime.ts

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+/** Normalize to local midnight; invalid input falls back to today. */
+export function startOfLocalDay(d: Date): Date {
+  if (Number.isNaN(d.getTime())) {
+    const t = new Date();
+    return new Date(t.getFullYear(), t.getMonth(), t.getDate(), 0, 0, 0, 0);
+  }
+  return new Date(d.getFullYear(), d.getMonth(), d.getDate(), 0, 0, 0, 0);
+}
+
+/** Local calendar bounds for a date (browser timezone). */
+export function getLocalDayIsoRange(day: Date): { from: string; to: string } {
+  const start = startOfLocalDay(day);
+  const end = new Date(start.getFullYear(), start.getMonth(), start.getDate() + 1, 0, 0, 0, 0);
+  return { from: start.toISOString(), to: end.toISOString() };
+}
+
+export function toDateInputValue(d: Date): string {
+  const y = d.getFullYear();
+  const m = String(d.getMonth() + 1).padStart(2, '0');
+  const day = String(d.getDate()).padStart(2, '0');
+  return `${y}-${m}-${day}`;
+}
+
+export function parseDateInput(value: string): Date {
+  const [y, m, d] = value.split('-').map(Number);
+  return new Date(y, m - 1, d, 0, 0, 0, 0);
+}
+
+export function combineLocalDateAndTime(day: Date, timeHHmm: string): Date {
+  const [h, min] = timeHHmm.split(':').map(Number);
+  return new Date(day.getFullYear(), day.getMonth(), day.getDate(), h, min, 0, 0);
+}
+
+export function formatTimeForInput(d: Date): string {
+  const h = String(d.getHours()).padStart(2, '0');
+  const m = String(d.getMinutes()).padStart(2, '0');
+  return `${h}:${m}`;
+}
+
+export function isSameLocalCalendarDay(a: Date, b: Date): boolean {
+  return (
+    a.getFullYear() === b.getFullYear() &&
+    a.getMonth() === b.getMonth() &&
+    a.getDate() === b.getDate()
+  );
+}
+
+export function formatHourLabel(hour: number): string {
+  const d = new Date(2000, 0, 1, hour, 0, 0, 0);
+  return d.toLocaleTimeString(undefined, { hour: 'numeric', hour12: true });
+}
+
+/** Local midnight + delta calendar days. */
+export function addCalendarDays(day: Date, delta: number): Date {
+  return new Date(day.getFullYear(), day.getMonth(), day.getDate() + delta, 0, 0, 0, 0);
+}
+
+/** Compare two calendar days at local midnight (ordering by date only). */
+export function compareLocalDayStart(a: Date, b: Date): number {
+  const ta = new Date(a.getFullYear(), a.getMonth(), a.getDate()).getTime();
+  const tb = new Date(b.getFullYear(), b.getMonth(), b.getDate()).getTime();
+  return ta - tb;
+}

frontend/src/lib/formatApiError.ts

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+export function formatApiErrorMessage(err: unknown, fallback: string): string {
+  if (err && typeof err === 'object' && 'message' in err) {
+    const m = (err as { message: unknown }).message;
+    if (Array.isArray(m)) {
+      return m.filter(Boolean).join(', ');
+    }
+    if (typeof m === 'string' && m.trim()) {
+      return m;
+    }
+  }
+  return fallback;
+}