Contact Form: add deprecation warnings to Contact Form module codebase

[monsieur-z]

Fixes https://github.com/Automattic/jetpack/issues/35654

Proposed changes:

Add deprecation warnings to the global functions, classes, public methods, and properties in the Contact Form module codebase. The code has been brought over to the Forms package.

This PR also updates some Jetpack plugin tests to reference the Forms package instead of the Contact Form module. Indeed, the deprecation warnings added to the module made many tests fail.

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

Project thread: pf5801-Aj-p2

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

No.

Testing instructions:

There's not much to test here.

• Spin up a test site with this branch
• Make sure you have access to the server logs
• Use the Contact Form module instead of the Forms package by ensuring the condition at this line is falsy: https://github.com/Automattic/jetpack/blob/trunk/projects/plugins/jetpack/modules/contact-form.php#L33
• Verify you see the deprecation warnings in the logs

[github-actions[bot]]

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 WordPress.com Simple 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, and enable the update/contact-form-module-depreacted-fn branch.

• To test on Simple, run the following command on your sandbox:

  bin/jetpack-downloader test jetpack update/contact-form-module-depreacted-fn
  

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[bot]]

Thank you for your PR!

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

• :white_check_mark: Include a description of your PR changes.
  
• :white_check_mark: Add a "[Status]" label (In Progress, Needs Team Review, ...).
  
• :white_check_mark: Add testing instructions.
  
• :white_check_mark: Specify whether this PR includes any changes to data or privacy.
  
• :white_check_mark: 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 :robot:

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The e2e test report can be found here. Please note that it can take a few minutes after the e2e tests checks are complete for the report to be available.

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Once your PR is ready for review, check one last time that all required checks appearing at the bottom of this PR are passing or skipped. Then, add the "[Status] Needs Team Review" label and ask someone from your team review the code. Once reviewed, it can then be merged. If you need an extra review from someone familiar with the codebase, you can update the labels from "[Status] Needs Team Review" to "[Status] Needs Review", and in that case Jetpack Approvers will do a final review of your PR.

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Jetpack plugin:

The Jetpack plugin has different release cadences depending on the platform:

• WordPress.com Simple releases happen daily.
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