Forms: Add error codes on ajax submission failure response

[dhasilva]

This is to help track down FORMS-248, as we can't reproduce the issue so far.

Proposed changes:

Adds error codes to the request response on failure so we can narrow down the cause of the issue.

Other information:

• Have you written new tests for your changes, if applicable?
• Have you checked the E2E test CI results, and verified that your changes do not break them?
• Have you tested your changes on WordPress.com, if applicable (if so, you'll see a generated comment below with a script to run)?

Jetpack product discussion

Does this pull request change what data or activity we track or use?

Testing instructions:

The intent is to have no change on normal operation.

• Check that tests pass
• Check that there is no regression
• Locally, force a submission failure and check the response on the network tab of the developer console
• Check that there is an error code that points to where the failure happened

[github-actions]

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