build: migrate eslint to v10 flat config and upgrade typescript

Replace .eslintrc.json with eslint.config.js using the new flat config
format required by ESLint 10. Swap @typescript-eslint/eslint-plugin and
@typescript-eslint/parser for the unified typescript-eslint package.
Upgrade TypeScript to 5.9 and @types/node to 25. Apply automatic code
fixes: remove unused catch bindings and preserve error cause in auth
header parsing.

eslint.config.mjs

@@ -0,0 +1,54 @@
+import { defineConfig } from "@eslint/config-helpers";
+import eslint from "@eslint/js";
+import tseslint from "typescript-eslint";
+import eslintConfigPrettier from "eslint-config-prettier";
+import globals from "globals";
+
+export default defineConfig(
+  {
+    ignores: ["dist/", "test/*.js"],
+  },
+  eslint.configs.recommended,
+  ...tseslint.configs.recommended,
+  eslintConfigPrettier,
+  {
+    languageOptions: {
+      globals: {
+        ...globals.es2022,
+        ...globals.node,
+      },
+      parserOptions: {
+        projectService: true,
+        tsconfigRootDir: import.meta.dirname,
+      },
+    },
+    rules: {
+      "no-shadow": ["error", { allow: ["err"] }],
+      "handle-callback-err": "error",
+      "prefer-arrow-callback": "error",
+      "no-buffer-constructor": "error",
+      "prefer-const": ["error", { destructuring: "all" }],
+      eqeqeq: ["error", "always", { null: "ignore" }],
+      "@typescript-eslint/no-explicit-any": "off",
+      "@typescript-eslint/no-use-before-define": [
+        "error",
+        { functions: false },
+      ],
+      "@typescript-eslint/explicit-function-return-type": [
+        "error",
+        { allowExpressions: true },
+      ],
+      "@typescript-eslint/no-floating-promises": "error",
+      "@typescript-eslint/no-misused-promises": "error",
+      "no-prototype-builtins": "off",
+    },
+  },
+  {
+    files: ["ui/**/*.ts", "ui/**/*.tsx"],
+    languageOptions: {
+      globals: {
+        ...globals.browser,
+      },
+    },
+  },
+);