Enhancement: [no-misused-promises or no-floating-promises or await-thenable?] should prohibit using a sync disposable with `await using`

Before You File a Proposal Please Confirm You Have Done The Following...

[X] I have searched for related issues and found none that match my proposal.
[X] I have searched the current rule list and found no rules that match my proposal.
[X] I have read the FAQ and my problem is not listed.

My proposal is suitable for this project

[X] I believe my proposal would be useful to the broader TypeScript community (meaning it is not a niche proposal).

Link to the rule's documentation

https://typescript-eslint.io/rules/await-thenable/, https://typescript-eslint.io/rules/no-floating-promises, https://typescript-eslint.io/rules/no-misused-promises

Description

I would like to find a place to lint for providing a sync disposable to an await using statement. This relates closely to https://github.com/typescript-eslint/typescript-eslint/issues/8858, so maybe await-thenable is the right place for this check? But it also has concerns very adjacent to no-floating-promises and no-misused-promises, so I'm not sure.

Fail

async function unhandledRejection() {             
    await using _ = {
        async [Symbol.dispose]() {
            throw new Error('dispose error');
        }
    }
}

Pass

async function properlyHandledRejection() {             
    await using _ = {
        async [Symbol.asyncDispose]() {
            throw new Error('dispose error');
        }
    }
}

Additional Info

The promise rejection in unhandledRejection cannot be caught, since the [Symbol.dispose]() method is called, but is not awaited, by an await using statement. Only the [Symbol.asyncDispose]() method is awaited.

There's a lot of subtlety here so I've provided a repo to be able to play with variations on this at https://github.com/kirkwaiblinger/typescript-eslint-repro-await-using

typescript-eslint / typescript-eslint