feat: enhance new-patient AI chat flow with full scheduling and eligibility

- Add 3-message intro (self-intro → empathetic ack → new/existing question) via single TwiML response to guarantee delivery order
- Detect reschedule intent from first message; look up existing appointment date
- New patient flow: ask insurance type → MassHealth consent → member ID + DOB → Selenium eligibility check
- Post-eligibility: active → ask appointment date/time with office-hours validation; inactive → ask other insurance or collect contact info
- Date/time collection mirrors reschedule flow: check office day open, ask time, validate against office hours
- Auto-create appointment in schedule for known patients on confirmation; use first available staff member
- Add openPhoneReply toggle (Settings → AI Chat) to respond to any number at any time
- Add 5-minute inactivity timeout: reset conversation to initial stage and clear pending state
- Normalize MassHealth DOB to zero-padded MM/DD/YYYY before Selenium submission
- Expand isExistingPatient classifier to recognize "old patient", "old", "previous", "prior"
- Existing patient confirmation message now acknowledges patient type before asking about insurance

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

apps/Backend/src/ai/reschedule-graph.ts

@@ -58,7 +58,7 @@ function getNextWeekDateObjects() {
 }
 
 /** Format "HH:MM" (24-h) → "H:MM am/pm" */
-function timeLabel(hhmm: string): string {
+export function timeLabel(hhmm: string): string {
   const [h, m] = hhmm.split(":").map(Number);
   const h12 = (h! % 12) || 12;
   const ampm = (h! >= 12) ? "pm" : "am";
@@ -80,7 +80,7 @@ function messageHasTime(msg: string): boolean {
  * Parse only a date (no time) from a message like "5/18" or "next Monday".
  * Returns a UTC-midnight Date and a date-only display label, or null.
  */
-async function parseDateOnlyFromMessage(
+export async function parseDateOnlyFromMessage(
   message: string,
   apiKey: string,
 ): Promise<{ date: Date; dateLabel: string } | null> {
@@ -249,7 +249,7 @@ Rules:
  * Returns true if the given date+time is within the office's configured hours.
  * Falls back to true (unrestricted) if no hours are configured.
  */
-async function isWithinOfficeHours(
+export async function isWithinOfficeHours(
   date: Date,
   time: string,
   userId: number,
@@ -285,7 +285,7 @@ async function isWithinOfficeHours(
  * Returns whether the office is open at all on a given date (day-level check).
  * Also returns the display day name (e.g. "Sunday") for use in error messages.
  */
-async function isOfficeDayOpen(
+export async function isOfficeDayOpen(
   date: Date,
   userId: number,
 ): Promise<{ open: boolean; displayDay: string }> {
@@ -319,7 +319,7 @@ async function isOfficeDayOpen(
  * e.g. "9:00 am – 12:00 pm and 1:00 pm – 5:00 pm".
  * Returns null if no hours are configured or the day is closed.
  */
-async function getOfficeHoursDisplay(date: Date, userId: number): Promise<string | null> {
+export async function getOfficeHoursDisplay(date: Date, userId: number): Promise<string | null> {
   try {
     const record = await storage.getOfficeHours(userId);
     if (!record?.data) return null;
@@ -387,7 +387,7 @@ async function isSlotAvailable(
 
 // ── Time parsing (legacy) ─────────────────────────────────────────────────────
 
-async function parseTime(message: string, apiKey: string): Promise<string | null> {
+export async function parseTime(message: string, apiKey: string): Promise<string | null> {
   const t = message.toLowerCase();
   if (/\bmorning\b|mañana|manhã|上午|صباح|maten/i.test(t))   return "09:00";
   if (/\bafternoon\b|tarde|après-midi|下午|مساء|aprèmidi/i.test(t)) return "13:00";