Support "Flat Config" (ESLint 9)

[JoshuaKGoldberg]

👋 Coming over from eslint/eslint#18093: ESLint is migrating to a new "flat config" format that will be the default in ESLint v9.

I tried this extension out in a repository with the new eslint.config.js (https://github.com/eslint/create-config) and got an error for a configuration not found:

/Users/josh/repos/create-config/node_modules/eslint/node_modules/@eslint/eslintrc/dist/eslintrc.cjs:4000
            throw new ConfigurationNotFoundError(directoryPath);
                  ^

ConfigurationNotFoundError: No ESLint configuration found in /Users/josh/repos/create-config/lib/shared.
    at CascadingConfigArrayFactory._finalizeConfigArray (/Users/josh/repos/create-config/node_modules/eslint/node_modules/@eslint/eslintrc/dist/eslintrc.cjs:4000:19)
    at CascadingConfigArrayFactory.getConfigArrayForFile (/Users/josh/repos/create-config/node_modules/eslint/node_modules/@eslint/eslintrc/dist/eslintrc.cjs:3791:21)
    ...

I'm posting this issue here as a reference & cross-linking it to the table in eslint/eslint#18093. If there's anything blocking the extension from supporting flat configs, please let us know - we'd be happy to try to help! 💜

Additional resources:

• Configuration Migration Guide
• (edit) Plugin Migration to Flat Config
• Blog posts on the new config system: Part 1: Background, Part 2: Introduction to flat config