chore: bump typescript-eslint to v7

[JoshuaKGoldberg]

Pre-flight checklist

• [x] I have read the Contributing Guidelines on pull requests.
• ~[ ] If this is a code change: I have written unit tests and/or added dogfooding pages to fully verify the new behavior.~
• ~[ ] If this is a new API or substantial change: the PR has an accompanying issue (closes #0000) and the maintainers have approved on my working plan.~

Motivation

👋 Hi! I'm coming over from https://github.com/typescript-eslint/typescript-eslint/issues/9141: I'd like to try out the new typescript-eslint v8 version in beta now... but Docusaurus is still on v5. This PR gets you to the latest stable version, v7, without making any other substantial changes.

Test Plan

yarn lint
yarn build

Test links

n/a - should be no functional code changes.

Related issues/PRs

None exist, but if you'd like I'm happy to file any issues you'd want! ❤️