Compatibility with new eslint config spec

Eslint announced a new config spec.
https://eslint.org/docs/latest/user-guide/configuring/configuration-files-new

According to [eslint's official blog](https://eslint.org/blog/2022/08/new-config-system-part-2/), though backward compatibility was taken care of, not all shareable configs continue to work with the new config system.

Are `eslint-config-airbnb-base` and `eslint-config-airbnb` compatible with the new config?

Thanks.

Start with the new ESLint configuration specification and the official blog linked in the issue. Then inspect eslint-config-airbnb-base and eslint-config-airbnb against the new config system, recording whether each remains compatible and what changes, if any, are required. Done means the compatibility question has a verified, documented answer.

Written by the indexing model from the issue text.