chore(test): install and configure vitest eslint plugin (#3228)

Co-authored-by: N. Taylor Mullen <ntaylormullen@google.com>

package-lock.json

@@ -26,6 +26,7 @@
         "@types/mock-fs": "^4.13.4",
         "@types/shell-quote": "^1.7.5",
         "@vitest/coverage-v8": "^3.1.1",
+        "@vitest/eslint-plugin": "^1.3.4",
         "concurrently": "^9.2.0",
         "cross-env": "^7.0.3",
         "esbuild": "^0.25.0",
@@ -3386,6 +3387,29 @@
         }
       }
     },
+    "node_modules/@vitest/eslint-plugin": {
+      "version": "1.3.4",
+      "resolved": "https://registry.npmjs.org/@vitest/eslint-plugin/-/eslint-plugin-1.3.4.tgz",
+      "integrity": "sha512-EOg8d0jn3BAiKnR55WkFxmxfWA3nmzrbIIuOXyTe6A72duryNgyU+bdBEauA97Aab3ho9kLmAwgPX63Ckj4QEg==",
+      "dev": true,
+      "license": "MIT",
+      "dependencies": {
+        "@typescript-eslint/utils": "^8.24.1"
+      },
+      "peerDependencies": {
+        "eslint": ">= 8.57.0",
+        "typescript": ">= 5.0.0",
+        "vitest": "*"
+      },
+      "peerDependenciesMeta": {
+        "typescript": {
+          "optional": true
+        },
+        "vitest": {
+          "optional": true
+        }
+      }
+    },
     "node_modules/@vitest/expect": {
       "version": "3.2.4",
       "resolved": "https://registry.npmjs.org/@vitest/expect/-/expect-3.2.4.tgz",