What I've found so far in my research:
* next lint --config eslint.config.js returns an error that suggests it's trying to parse the config file as an older format.
* In the event I do get it to work, next lint is hooked into next build, so if I don't update next lint to use the new config file, next build may build even when the linter fails (https://nextjs.org/docs/pages/api-reference/next-config-js/eslint)

My goal is to load a plugin I've written locally. The docs for ESLint say that I need the new flat eslint.config.js format: https://eslint.org/docs/latest/extend/custom-rule-tutorial#step-8-use-the-plugin-locally Maybe there's another way to do it, or maybe I just bite the bullet and package my plugin so I can use the old format?

next lint --rulesdir works! The three major downsides I've found so far are that:

1. rulesdir is deprecated
2. VS Code has no idea I've set rulesdir
3. Neither does next build, so a linter fail won't stop the build.

i suggest you make a bug report in https://github.com/vercel/next.js

Good idea; I should let the team know. I ended up packaging my custom rule in a plugin so I could use it with the old config file format.