Retrieve Chrome AI tokens from AI Assistant features (#43442)

* Retrieve Chrome AI tokens from WPCOM

* changelog

* Move Origin Trials token injection to the frontend

The previous approach wasn't working since it was being done too early
in the lifecycle. I've moved it to the frontend after the AI Features
have been retrieved.

* changelog

Committed via a GitHub action: https://github.com/Automattic/jetpack/actions/runs/15070215046

Upstream-Ref: Automattic/jetpack@96f58a7

Author: vianasw

package.json

@@ -31,7 +31,7 @@
 		"@automattic/jetpack-api": "^0.20.2",
 		"@automattic/jetpack-components": "^0.73.0",
 		"@automattic/jetpack-connection": "^0.39.14",
-		"@automattic/jetpack-shared-extension-utils": "^0.19.3",
+		"@automattic/jetpack-shared-extension-utils": "^0.20.0-alpha",
 		"@automattic/number-formatters": "^1.0.1",
 		"@tanstack/react-query": "5.75.1",
 		"@wordpress/api-fetch": "7.22.0",