[eprh] Fix `recommended` config for flat config compatibility

Previously, the `recommended` config used the legacy ESLint format (plugins as an array of strings). This causes errors when used with ESLint v9's `defineConfig()` helper. This was following [eslint's own docs](https://eslint.org/docs/latest/extend/plugins#backwards-compatibility-for-legacy-configs):

> With this approach, both configuration systems recognize "recommended". The old config system uses the recommended key while the current config system uses the flat/recommended key. The defineConfig() helper first looks at the recommended key, and if that is not in the correct format, it looks for the flat/recommended key. This allows you an upgrade path if you’d later like to rename flat/recommended to recommended when you no longer need to support the old config system.

However, [`isLegacyConfig()`](https://github.com/eslint/rewrite/blob/main/packages/config-helpers/src/define-config.js#L73-L81) (also see [`eslintrcKeys`](https://github.com/eslint/rewrite/blob/main/packages/config-helpers/src/define-config.js#L24-L35)) function doesn't check for the `plugins` key, so our config was incorrectly treated as flat config despite being in legacy format.

This PR fixes the issue, along with a few other fixes combined:

1. Convert `recommended` to flat config format
2. Separate basic rules (exhaustive-deps, rules-of-hooks) from compiler rules
3. Add `recommended-latest-legacy` config for non-flat config users who want all recommended rules (including compiler rules)
4. Adding more types for the exported config

Our shipped presets in 6.x.x will essentially be:
- `recommended-legacy`: legacy (non-flat), with basic rules only
- `recommended-latest-legacy`: legacy (non-flat), all rules (basic + compiler)
- `flat/recommended`: flat, basic rules only (now the same as recommended, but to avoid making a breaking change we'll just keep it around in 6.x.x)
- `recommended-latest`: flat, all rules (basic + compiler)
- `recommended`: flat, basic rules only

In the next breaking release 7.x.x, we will collapse down the presets into three:

- `recommended-legacy`: all recommended rules
- `recommended`: all recommended rules
- `recommended-experimental`: all recommended rules + new bleeding edge experimental rules

Closes #34679