My Jetpack: add connection animation (#40343)

* My Jetpack: add new loading logic to My Jetpack

* changelog

* Add animation

* Adjust animation rhythm

* Fix sentences

* Adjust duration of the connected screen

* Adjust error handling and spacing

* Reset notices when initializing site connection

Committed via a GitHub action: https://github.com/Automattic/jetpack/actions/runs/12111138664

Upstream-Ref: Automattic/jetpack@7489029

composer.json

@@ -8,7 +8,7 @@
 		"automattic/jetpack-admin-ui": "^0.5.1",
 		"automattic/jetpack-assets": "^4.0.0",
 		"automattic/jetpack-connection": "^6.1.0",
-		"automattic/jetpack-my-jetpack": "^5.0.5-alpha",
+		"automattic/jetpack-my-jetpack": "^5.1.0-alpha",
 		"automattic/jetpack-plans": "^0.5.1"
 	},
 	"require-dev": {