fix: resolve lint errors and xlarge mismatch for dev→uat promotion

- Remove unused gte/lt/ne imports from cascade.ts
- Prefix unused params originalEndTime, originalStartTime, newStartTime
  with underscore in cascade.ts and appointments.ts callers
- Remove unused petCoatType query param from book.ts availability route
- Align xlarge value: Book.tsx now uses "xlarge" (no hyphen) everywhere
  to match the Zod booking schema

Co-Authored-By: Paperclip <noreply@paperclip.ing>

apps/api/src/routes/book.ts

@@ -44,7 +44,6 @@ bookRouter.get("/availability", async (c) => {
   const serviceId = c.req.query("serviceId");
   const dateStr = c.req.query("date");
   const petSizeCategory = c.req.query("petSizeCategory") ?? undefined;
-  const petCoatType = c.req.query("petCoatType") ?? undefined;
 
   if (!serviceId || !dateStr) {
     return c.json({ error: "serviceId and date are required" }, 400);