Podcast: move SPA, REST settings, and feed customization into the package (4/4)

[arcangelini]

PR 4 of 4 in the Podcast untangle train.

Proposed changes

Drops the wp-build placeholder dashboard from PR 3 in favor of the proven webpack-built SPA from #48499 and brings in the rest of the feature: REST settings glue (Settings_REST), feed customization (Customize_Feed / Feed_Detection / App_Detection), and the four real tab implementations (Welcome, Settings, Episodes, Distribution) with their hooks, components, and podcast-apps registry. Still gated behind jetpack_podcast_untangle — Simple/Atomic only and no behavior change while the filter is off.

The wp-build pattern from PR 2/3 stays available for a future port; this PR opts for webpack so the existing SPA from #48499 lands intact rather than getting re-architected mid-train.

Stacked on #48559. Replaces #48499 once green.

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

No.

Testing instructions

TBD.

[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 or WordPress.com Site Helper), and enable the add/podcast-business-code branch.
• To test on Simple, run the following command on your sandbox:

bin/jetpack-downloader test jetpack add/podcast-business-code

bin/jetpack-downloader test jetpack-mu-wpcom-plugin add/podcast-business-code

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]

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Follow this PR Review Process:

1. Ensure all required checks appearing at the bottom of this PR are passing.
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Jetpack plugin:

No scheduled milestone found for this plugin.

If you have any questions about the release process, please ask in the #jetpack-releases channel on Slack.

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Mu Wpcom plugin:

• Next scheduled release: WordPress.com Simple releases happen semi-continuously (PCYsg-Jjm-p2)

If you have any questions about the release process, please ask in the #jetpack-releases channel on Slack.

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Wpcomsh plugin:

• Next scheduled release: Atomic deploys happen twice daily on weekdays (p9o2xV-2EN-p2)

If you have any questions about the release process, please ask in the #jetpack-releases channel on Slack.

[jp-launch-control]

Code Coverage Summary

No summary data is available for parent commit 99a0f0d, so cannot calculate coverage changes. 😴

If that commit is a feature branch rather than a trunk commit, this is expected. Otherwise, this should be updated once coverage for 99a0f0d is available.

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