Forms: Update on submit to use new feedback class.

[enejb]

This PR update the form submission data to use the new Feedback class.

This PR breaks #44462 into smaller more testable pieces.

Proposed changes:

• Deprecates the get_json_data method.
• Deprecates the get_raw_compiled_form_data $form parameter. Since it is no longer needed.

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)?

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

No

Testing instructions:

1. Fill out the form. Notice that it still works as expected.
2. Update the add_filter( 'jetpack_forms_enable_ajax_submission', '__return_true' ); filter. Notice that it still works as expected.
3. Notice that the emails that get created still work look like before.

[github-actions]

Are you an Automattician? Please test your changes on all WordPress.com environments to help mitigate accidental explosions.

• To test on WoA, go to the Plugins menu on a WoA dev site. Click on the "Upload" button and follow the upgrade flow to be able to upload, install, and activate the Jetpack Beta plugin. Once the plugin is active, go to Jetpack > Jetpack Beta, select your plugin (Jetpack), and enable the update/forms-on-submit-use-feedback branch.
• To test on Simple, run the following command on your sandbox:

bin/jetpack-downloader test jetpack update/forms-on-submit-use-feedback

Interested in more tips and information?

• In your local development environment, use the jetpack rsync command to sync your changes to a WoA dev blog.
• Read more about our development workflow here: PCYsg-eg0-p2
• Figure out when your changes will be shipped to customers here: PCYsg-eg5-p2

[github-actions]

Thank you for your PR!

When contributing to Jetpack, we have a few suggestions that can help us test and review your patch:

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• ✅ Add a "[Status]" label (In Progress, Needs Review, ...).
  
• ✅ Add a "[Type]" label (Bug, Enhancement, Janitorial, Task).
  
• ✅ Add testing instructions.
  
• ✅ Specify whether this PR includes any changes to data or privacy.
  
• ✅ Add changelog entries to affected projects
  

This comment will be updated as you work on your PR and make changes. If you think that some of those checks are not needed for your PR, please explain why you think so. Thanks for cooperation 🤖

---

Follow this PR Review Process:

1. Ensure all required checks appearing at the bottom of this PR are passing.
2. Make sure to test your changes on all platforms that it applies to. You're responsible for the quality of the code you ship.
3. You can use GitHub's Reviewers functionality to request a review.
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[jp-launch-control]

Code Coverage Summary

Coverage changed in 1 file.

File	Coverage	Δ%	Δ Uncovered
projects/packages/forms/src/contact-form/class-contact-form.php	582/1087 (53.54%)	-1.05%	-14 💚

Full summary · PHP report · JS report

[CGastrell]

Worked well!