Switch to ESLInt flatconfig

[pmcelhaney]

Migrate to the new "flatconfig" configuration format, which is the default for ESLint 9.

#839

I'm not sure if we can switch to the new format before all of the dependencies are switched over. If not, it will probably be a long time before we can switch. But we should set the environment variable that causes ESLint to use the old format so we can stay on the latest version.

I wonder if we can throw the old file at ChatGPT and ask it to output the new format.

[dethell]

I took a shot at having Copilot convert the file, but it wasn't right. Maybe a good starting point, but not a working conversion.