feat: batch eligibility by patient name + "Check All & Appointment Today" option

- Add batch_eligibility_by_name intent so "check Mary and Sinthia" resolves multiple names
- Add "Check All & Appointment Today" button to batch eligibility UI — creates appointment for each patient after their eligibility check completes

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

apps/Backend/src/ai/internal-chat-graph.ts

@@ -6,6 +6,7 @@ export type InternalChatIntent =
   | "check_eligibility"     // by patient name → look up in DB
   | "eligibility_by_id"     // by explicit memberId + dob (no name)
   | "batch_eligibility"     // multiple patients by memberId + dob
+  | "batch_eligibility_by_name" // multiple patients by name (no memberId)
   | "batch_claim"           // claim same procedures for multiple patients by name
   | "batch_check_and_claim" // eligibility + claim for multiple patients by memberId+dob
   | "check_and_claim"       // eligibility + claim procedures
@@ -81,6 +82,11 @@ Intents:
                           e.g. "check 100xxxx, 10/10/1988 and 200xxxx, 5/5/2000"
                           Use this ONLY when TWO OR MORE distinct memberId+dob pairs are given.
                           Put each pair into the "patients" array. Also set insuranceHint if stated.
+- batch_eligibility_by_name : user wants to check eligibility for MULTIPLE patients identified by NAME
+                          e.g. "check Mary and Sinthia", "check eligibility for John, Jane, and Bob"
+                          e.g. "verify insurance for Mary and Sinthia"
+                          Use this when TWO OR MORE patient names are given WITHOUT member IDs.
+                          Put each patient name into the "patientNames" array.
 - batch_claim           : user wants to claim the SAME procedures for MULTIPLE patients identified by NAME
                           e.g. "claim perio exam and adult prophy for Jackaline and Keioson"
                           e.g. "perio exam, adult cleaning for Maria and John"