fix: resolve all TypeScript type errors

- Install missing comlink (was in lockfile but not node_modules)
- Add @ts-rest/core and @ts-rest/vue-query (imported but not declared as deps)
- Add declare module '*.vue' shim to shims-vue.d.ts
- Replace arktype validators in ts-rest contract with contract.type<T>() since @ts-rest expects Zod schemas

package.json

@@ -28,6 +28,8 @@
     "@tailwindcss/postcss": "^4.1.16",
     "@tanstack/vue-query": "^5.92.9",
     "@toycode/markdown-it-class": "^1.2.4",
+    "@ts-rest/core": "^3.52.1",
+    "@ts-rest/vue-query": "^3.52.1",
     "@vscode/markdown-it-katex": "^1.1.2",
     "@vueuse/components": "^14.2.1",
     "@vueuse/core": "^13.6.0",