feat: batch eligibility, batch claim, and batch check+claim from AI chat

- Add batch_eligibility, batch_claim, and batch_check_and_claim intents
  to AI classifier so multiple patients can be processed one by one
- Add queue processing on insurance-status and claims pages to auto-start
  the next patient after each check/claim completes
- Make patient schema firstName, lastName, phone optional so patients can
  be created with just member ID + DOB from eligibility checks
- Cancel buttons now preserve chat history instead of clearing it
- Patient-found card shows Check Eligibility, Eligibility & Appointment
  Today, and Cancel buttons
- Claim service date asks user to pick between latest appointment and
  today when they differ
- Login page subtitle styled with animated gradient

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

packages/db/types/patient-types.ts

@@ -51,14 +51,14 @@ export const insertPatientSchema = (
     createdAt: true,
   })
   .extend({
-    firstName: z.string().min(1, "First name is required"),
-    lastName: z.string().min(1, "Last name is required"),
+    firstName: z.string().optional().default(""),
+    lastName: z.string().optional().default(""),
     dateOfBirth: z.preprocess(
       (val) => (val === null || val === undefined || val === "" ? undefined : val),
       z.coerce.date({ required_error: "Date of birth is required" })
     ),
     gender: z.string().optional().nullable(),
-    phone: z.string().min(1, "Phone number is required"),
+    phone: z.string().optional().nullable(),
     insuranceId: insuranceIdSchema,
   });