fix: resolve all typecheck, lint, and test failures

- Add @types/node to packages/db devDependencies (typecheck was missing process)
- Re-export drizzle-orm helpers (eq, gte, etc.) from @groombook/db to avoid
  duplicate-instance type conflicts; remove drizzle-orm direct dep from API
- Add @hono/zod-validator and jose as direct API dependencies
- Merge duplicate @groombook/db imports in all route files
- Fix noUncheckedIndexedAccess errors: appointments PATCH, web calendar grid
- Fix weightKg/dateOfBirth type conversion in pets route (numeric→string, string→Date)
- Add eslint.config.js for API and web (ESLint 9 flat config format)
- Add vitest.config.ts with passWithNoTests for API and web

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

packages/db/package.json

@@ -15,6 +15,7 @@
     "postgres": "^3.4.5"
   },
   "devDependencies": {
+    "@types/node": "^22.10.7",
     "drizzle-kit": "^0.30.4",
     "typescript": "^5.7.3"
   }

packages/db/src/index.ts

@@ -3,6 +3,7 @@ import postgres from "postgres";
 import * as schema from "./schema.js";
 
 export * from "./schema.js";
+export { and, asc, desc, eq, gte, gt, lt, lte, ne, or, sql } from "drizzle-orm";
 
 let _db: ReturnType<typeof drizzle> | null = null;