feat: add ESLint, lint-staged, and update pre-commit hook + CI

- Add ESLint 9 flat config (eslint.config.mjs) with typescript-eslint
  recommended rules and eslint-config-prettier
- Add lint-staged to run eslint+prettier only on staged files
- Update pre-commit hook to use lint-staged instead of full prettier check
- Add `lint` and `format:check` scripts to package.json
- Add Lint step to CI workflow
- Fix resulting lint errors: unused vars (_ctx, _options, catch binding),
  any→unknown in type declarations, stale eslint-disable comments

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

eslint.config.mjs

@@ -0,0 +1,22 @@
+import prettier from "eslint-config-prettier";
+import tseslint from "typescript-eslint";
+
+export default tseslint.config(
+  { ignores: ["dist/", "coverage/"] },
+  ...tseslint.configs.recommended,
+  prettier,
+  {
+    rules: {
+      "@typescript-eslint/no-unused-vars": [
+        "error",
+        { argsIgnorePattern: "^_", varsIgnorePattern: "^_" },
+      ],
+    },
+  },
+  {
+    files: ["src/**/*.test.ts", "src/test/**/*.ts"],
+    rules: {
+      "@typescript-eslint/no-explicit-any": "off",
+    },
+  },
+);