test: use latest `typescript-eslint` in examples

[mdjermanovic]

Updates examples/typescript test project to use the new package typescript-eslint that supports flat config.

Note that @typescript-eslint/parser and @typescript-eslint/eslint-plugin are dependencies of typescript-eslint so there's no need to install them separately.

Configuration in eslint.config.js is based on the first example from https://typescript-eslint.io/linting/configs.