eslint: switch to flat configuration

[BacLuc]

Eslint 9 uses a new configuration format by default (called "flat configuration"). So this PR would need some config changes before we can upgrade to eslint9.

For Nuxt, some further details are described here:
https://eslint.nuxt.com/guide/faq#package-disambiguation
https://eslint.nuxt.com/packages/module

And here is a eslint migration guide for the new config format:
https://eslint.org/docs/latest/use/configure/migration-guide

Originally posted by @usu in #5155 (comment)

Also, we shouldn't need to add @typescript-eslint/eslint-plugin to the dev dependencies anymore.

[BacLuc]

Proposal to resolve this:

1. switch to new format for all modules
   I would do this first, because i did not get the nuxt eslint helper modules to support both
2. Update to eslint 9

[manuelmeister]

Core Meeting Decision

1. We individually switch the format for each module
2. Update to eslint 9