chore: migrate ESLint config to flat config

[JoshuaKGoldberg]

PR Checklist

• Addresses an existing open issue: fixes 🛠 Repo: Rework ESLint config: flat config, separate Prettier plugin #5058
• That issue was marked as status: accepting prs
• Steps in CONTRIBUTING.md were taken

Overview

Migrates from the old .eslintrc.yml to a new eslint.config.js per the new ESLint flat config. Applies a few touchups in the process:

• Removes package.json references to ESLint plugins that weren't being used anymore
  • eslint-plugin-import: 🛠 Repo: Enable eslint-plugin-import in ESLint config #5062
  • eslint-plugin-node (now eslint-plugin-n): 🛠 Repo: Enable eslint-plugin-n in ESLint config #5063
  • eslint-plugin-promise: 🛠 Repo: Enable eslint-plugin-promise in ESLint config #5064
• Adds a standalone npm run lint script in the package.json
• Adds a GitHub Actions ci.yml that runs that lint script, per 🛠️ Repo: Switch automations to GitHub Actions (GHA) #4117
• Removes @babel/eslint-parser as it's not necessary
• Removes the prettier and semistandard plugins/configs

Intentionally doesn't extend from eslint:recommended, as that change is likely to cause a lot more noise. I split that out into #5061.

[coveralls]

coverage: 94.335%. remained the same
when pulling 5976e7c on JoshuaKGoldberg:eslint-config-flat
into 53a4baf on mochajs:master.

[voxpelli]

Will look into this, it's on my todo to do for standard

[Uzlopak]

LGTM

Just a merge conflict in package-lock.