Launch Site Flow Standardization: Add WP Admin Launchpad variations

[bogiii]

Fixes DATSCI-1179

Proposed changes

This PR standardizes the "Launch site" task in the WP Admin launchpad dashboard widget, under the calypso_standardized_site_launch_gating ExPlat experiment. It builds on the shared infrastructure introduced in #47705 (useLaunchSiteMutation, CelebrateLaunchModal in common/).

The launchpad widget's launch task now has three variants:

• Control: preserves existing behaviour — the launchpad package makes the API call, then redirects to ?celebrate-launch=true
• gated_site_launch: intercepts the task click and redirects to https://wordpress.com/start/launch-site?siteSlug=…&ref=wp-admin without making an API call
• ungated_site_launch: intercepts the task click, launches via useLaunchSiteMutation (handles both Simple and Atomic sites), and shows CelebrateLaunchModal in place

The interception is done via the onTaskClick prop of the @automattic/launchpad component — returning false prevents the launchpad's own API call from firing.

Other information

• Generate changelog entries for this PR (using AI).

Related product discussion/links

• datsci-optimization-site-launch-standardization-b99113373d42

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

No.

Testing instructions

Prerequisites: An unlaunched Simple or Atomic site with an active launchpad checklist in the WP Admin dashboard. Assign the site to a variation of the calypso_standardized_site_launch_gating ExPlat experiment.

Control (no experiment assignment):

1. Go to WP Admin dashboard on an unlaunched site
2. Click "Launch" in the launchpad widget
3. Verify the site launches and the page reloads with ?celebrate-launch=true

gated_site_launch variation:

1. Same setup as above
2. Click "Launch" in the launchpad widget
3. Verify no API call is made and the user is redirected to wordpress.com/start/launch-site?siteSlug=…&ref=wp-admin

ungated_site_launch variation:

1. Same setup as above
2. Click "Launch" in the launchpad widget
3. Verify the site is launched via a back-end request (no redirect)
4. Verify the CelebrateLaunchModal appears in place with the correct domain, plan upsell, and "View site" link
5. Verify closing the modal stays on the same page

[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 (WordPress.com Site Helper), and enable the datsci-1179-standardize-site-launch-wp-admin-launchpad-task-entry-point-2 branch.
• To test on Simple, run the following command on your sandbox:

bin/jetpack-downloader test jetpack-mu-wpcom-plugin datsci-1179-standardize-site-launch-wp-admin-launchpad-task-entry-point-2

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