fix: resolve appointment form validation and socket connection issues

- Fix status enum in browser.ts (uppercase → lowercase values)
- Fix date validation (z.string → z.coerce.date) so form accepts Date objects
- Add missing type/userId/title fields to browser.ts appointment schema
- Replace nested PatientSearch Select with simple inline Input to fix patient selection
- Fix mutationFn to throw on non-ok responses so backend errors surface correctly
- Connect socket.io directly to backend (port 5000) instead of Vite proxy to fix AggregateError on startup

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

packages/db/usedSchemas/browser.ts

@@ -107,12 +107,15 @@ export const StaffUncheckedCreateInputObjectSchema = z.object({
 export const AppointmentUncheckedCreateInputObjectSchema = z.object({
   id: z.number().int().optional(),
   patientId: z.number().int(),
+  userId: z.number().int().optional(),
   staffId: z.number().int().optional(),
-  date: z.string(),
+  title: z.string().optional(),
+  date: z.coerce.date(),
   startTime: z.string(),
   endTime: z.string(),
+  type: z.string(),
   status: z
-    .enum(["SCHEDULED", "COMPLETED", "CANCELLED", "NO_SHOW"])
+    .enum(["scheduled", "confirmed", "completed", "cancelled", "no-show"])
     .optional(),
   notes: z.string().optional(),
 });