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/aiHandoffStore.ts

@@ -8,11 +8,17 @@ export type ConversationStage =
   | "new_patient_greeted"
   | "asked_new_or_existing"
   | "asked_new_patient_insurance"
+  | "asked_new_or_reschedule"
+  | "asked_insurance_type"
+  | "asked_masshealth_check_consent"
   | "asked_existing_insurance"
   | "asked_appointment_time"
   | "awaiting_masshealth_info"
   | "asked_appointment_preference"
   | "asked_self_pay"
+  | "asked_other_insurance_after_inactive"
+  | "collecting_contact_info"
+  | "asked_new_appt_time_for_date"
   | "asked_reschedule_confirm"
   | "asked_reschedule_preference"
   | "asked_reschedule_asap"