Convert to ESLint 9 flat config and move to pnpm, use .mjs and new jest types

[SleeplessByte]

Related: exercism/javascript-test-runner#852

Similar to: exercism/typescript#1506

• Migrate to pnpm: means less space used, and installing can often be done without internet connection as long as you download the exercise first. This is something we discussed in the past (not specifically pnpm, but "how can we share dependencies", and this I think is a good way to do it, for now. If corepack gets removed in the future, our migration path is as "simple" as removing corepack from the calls. Everything keeps working.
• Upgrade to ESLint 9: This is a significant upgrade that uses a new config flat file format. We already have it on TypeScript, so I think we should be good.
• Upgrade SDKs: for VSCode integration when working with this repository.
• Sync
• Format files
• Fix .vscode files, upgrade all tests to new format
• Update workflows to Node LTS @ 20
• Fix lint issues
• Remove babel transpilation for common actions: We really don't need it anymore. Check https://node.green/#ES2022!
• Simplify changed files check: The new method is much faster and doesn't rely on the first page of items in the change dataset.

[SleeplessByte]

Okay. So.

This PR works and relies on exercism/javascript-test-runner#852, but I do not know if that PR will work as it requires the tmp directory to be mounted with exec on as that's where pnpm installs the executables.

My plan is:

1. test the test runner against a non-upgraded exercise solution (so one that expects npm instead of pnpm)
2. merge the test runner
3. try this online

If that works, mark this as ready and we are good to go! If it doesn't work, I will revert the test runner and message Jeremy.