Use authenticated web view for updating plugins if possible

[itsmeichigo]

Closes WOOMOB-549

Description

This PR updates the code points that open the wp-admin page for updating plugin to use the authenticated web view if possible. This helps avoid authenticating again.

Additionally, I improved the logic to show the plugin info screen for updating rather than showing the plugin list. cc @iamgabrielma as you expressed concerns in the past about this, but it seems to work fine from my testing. Let me know what you think.

Test Steps

• Pre-requisites: Set up a Jurassic Ninja site with an outdated version of WooCommerce by uploading the zip of an older version here.
• If you want to test the site with WPCom authenticated, ensure that SSO is enabled in Jetpack > My Jetpack > Products > Secure Sign On. Otherwise, you'll have to log in to wp-admin with site credentials.
• Navigate to Menu tab > Settings.
• Confirm that in the Plugins section, WooCommerce is displayed as outdated. Tap on that row and confirm that a web view is displayed and you're authenticated right away.
• Dismiss the web view and select Plugins. Tap the WooCommerce row again and confirm that you see an authenticated web view here too.
• Try updating the plugin from the web view if needed.

Screenshots

Simulator.Screen.Recording.-.iPhone.17.-.2025-12-11.at.19.02.29.mov

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• I have considered if this change warrants user-facing release notes and have added them to RELEASE-NOTES.txt if necessary.

[dangermattic]

	1 Warning
⚠️	This PR is assigned to the milestone 23.9. This milestone is due in less than 2 days. Please make sure to get it merged by then or assign it to a milestone with a later deadline.

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[wpmobilebot]

📲 You can test the changes from this Pull Request in WooCommerce iOS Prototype by scanning the QR code below to install the corresponding build.

	App Name	WooCommerce iOS Prototype
	Build Number	pr16448-9664b56
	Version	23.8
	Bundle ID	com.automattic.alpha.woocommerce
	Commit	9664b56
	Installation URL	4r86njmogtsvo

Automatticians: You can use our internal self-serve MC tool to give yourself access to those builds if needed.

[adborbas]

Nice 👍