Fix incorrect exitCode when eslint is called with --stdin

[shumphrey]

What issue does this pull request address?
#6677

What changes did you make? (Give an overview)
I removed the exitCode variable and made each block set process.exitCode directly.

Is there anything you'd like reviewers to focus on?
Confirm the exitCode is set correctly by running

echo var a | eslint --stdin --rule no-var:error --no-eslintrc --no-ignore && echo good!

<codegood should not get echoed after this patch is applied.

Previously exitCode was set at the end of bin/eslint.js but the callback
executed for --stdin was asynchronous.
The asynchronous callback was setting exitCode after process.exitCode
had already been assigned.

This removes the exitCode variable and just gets each block to set
process.exitCode directly.

[mention-bot]

@shumphrey, thanks for your PR! By analyzing the annotation information on this pull request, we identified @nzakas, @ilyavolodin and @alberto to be potential reviewers

[eslintbot]

Thanks for the pull request, @shumphrey! I took a look to make sure it's ready for merging and found some changes are needed:

• The commit summary needs to begin with a tag (such as Fix: or Update:). Please check out our guide for how to properly format your commit summary and update it on this pull request.
• Pull requests with code require an issue to be mentioned at the end of the commit summary, such as (fixes #1234). Please update the commit summary with an issue (file a new issue if one doesn't already exist).

Can you please update the pull request to address these?

(More information can be found in our pull request guide.)

[eslintbot]

Thanks for the pull request, @shumphrey! I took a look to make sure it's ready for merging and found some changes are needed:

• The commit summary needs to begin with a tag (such as Fix: or Update:). Please check out our guide for how to properly format your commit summary and update it on this pull request.
• Pull requests with code require an issue to be mentioned at the end of the commit summary, such as (fixes #1234). Please update the commit summary with an issue (file a new issue if one doesn't already exist).

Can you please update the pull request to address these?

(More information can be found in our pull request guide.)

[eslintbot]

LGTM

[nzakas]

Lgtm.

@eslint/eslint-tsc this seems important to get fixed and released. The fix is very small so shouldn't be a problem to merge for today's release. Thoughts?

[ilyavolodin]

I think we should merge it before the release.

[gyandeeps]

LGTM, waiting for others to review.