Migrate to flat config

[catrope]

ESLint has introduced a new config system that is optional in v8 but will be the only config system starting with ESLint v9. We should make this package compatible with both systems, so that consumers can migrate to the new config system ahead of ESLint's 9.0.0 release if they want to (for example, because they want to use their own custom lint rules, which is easier to do in the new config system).

Migration info: https://eslint.org/docs/latest/extend/plugin-migration-flat-config