chore: update stale links and use latest eslint

[lumirlumir]

Prerequisites checklist

• I have read the contributing guidelines.

AI acknowledgment

• I did not use AI to generate this PR.
• (If the above is not checked) I have reviewed the AI-generated content before submitting.

What is the purpose of this pull request?

This PR updates stale links and uses the latest eslint packages in package.json.

What changes did you make? (Give an overview)

• Some badges were stale, so it was always failing and broken:

• Some links were stale, so they were redirected to the updated links.

• Some descriptions referenced a script that isn't used anywhere (test:open-coverage).

• Some links didn't use the https protocol, so I updated them to use https.

• Updated eslint to the latest.

I've updated all of the above.

Related Issues

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Is there anything you'd like reviewers to focus on?

N/A

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