Forms: Start using the new feedback version v3

[enejb]

Reverts #44925

Following #44927

Proposed changes:

• Revert saving feedback into the new V3 format.

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:

Same as #44889

Add a new form. With all the fields does the data get stored in the new format?
Are you still able to see the data in the responses tab in the back end?
Are you able to see the data in export. Do you still get the email notification?
Do you notice any PHP Errors?

Test the form by submitting Unicode characters as well as new lines and notice that you see them in the backend as expected.

[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-switch-to-v3 branch.
• To test on Simple, run the following command on your sandbox:

bin/jetpack-downloader test jetpack update/forms-switch-to-v3

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 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.
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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	573/1047 (54.73%)	-0.56%	0 💚

Full summary · PHP report · JS report

[dhasilva]

LGTM, works as expected