Rules updates to come in isolated commits.

Closes #354.

The rule that comes with ESLint now handles numeric separators,
obsoleting the need for a TS-specific one. This rule has been
deprecated in (though not yet removed from) upstream.

This rule was renamed in v6 to clarify what it does.
With v8, the deprecated legacy alias has been removed.

- The Airbnb config has been moved to a peer dependency, so ESLint can resolve
  it in legacy configs without requiring users to manually install it.
- The full Airbnb configs have been added as an optional peer dependency.
- Since non-optional peer dependencies are installed by default, they have
  stopped being duplicated in the dev dependencies.
- The ESLint dependency has been bumped to the latest minor version.

- Explicitly note the lack of ESLint 9 support, link to tracking ticket.
- Provide flat configuration instructions (and recommend their use).
- Update instructions for NPM v7 automatically installing peer dependencies.
- Update configuration for use with typescript-eslint v8.
- Some restructuring for readability.
- Added instructions for removing formatting rules, since it's less simple
  with the ESLint stylistic rules (until the Prettier config gets updated).

Closes #307