Authenticated WebView improvement [Part 3]

[hichamboushaba]

Closes: #13467

Description

This PR builds on top of what was added in #13487 and adds an additional handling for WebView authentication to the atomic sites, it fixes an issue that I identified while testing the Product Previews in #13494, for more details on the issue itself check: pe5sF9-3QB-p2#comment-4374.

For the fix, now we do the following for non-admin URLs:

1. We handle the Bearer token authentication with WordPress.com.
2. Then we load the site login URL with the redirect.

With this PR, we now implement the whole flow as represented in this document pe5sF9-3Si-p2

Steps to reproduce

For testing, please test the TC1 in #13494 using an Atomic website.

Testing information

Confirm that the Authenticated WebView works well with non-admin URLs in atomic websites.

The tests that have been performed

^

• I have considered if this change warrants release notes and have added them to RELEASE-NOTES.txt if necessary. Use the "[Internal]" label for non-user-facing changes.

Reviewer (or Author, in the case of optional code reviews):

Please make sure these conditions are met before approving the PR, or request changes if the PR needs improvement:

• The PR is small and has a clear, single focus, or a valid explanation is provided in the description. If needed, please request to split it into smaller PRs.
• Ensure Adequate Unit Test Coverage: The changes are reasonably covered by unit tests or an explanation is provided in the PR description.
• Manual Testing: The author listed all the tests they ran, including smoke tests when needed (e.g., for refactorings). The reviewer confirmed that the PR works as expected on big (tablet) and small (phone) in case of UI changes, and no regressions are added.

[dangermattic]

	2 Errors
🚫	This PR is tagged with status: do not merge label(s).
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[wpmobilebot]

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

	App Name	WooCommerce-Wear Android
	Platform	⌚️ Wear OS
	Flavor	Jalapeno
	Build Type	Debug
	Commit	80506c6
	Direct Download	woocommerce-wear-prototype-build-pr13505-80506c6.apk

[wpmobilebot]

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

	App Name	WooCommerce Android
	Platform	📱 Mobile
	Flavor	Jalapeno
	Build Type	Debug
	Commit	80506c6
	Direct Download	woocommerce-prototype-build-pr13505-80506c6.apk

[irfano]

2. Change the visibility of the product to private.
3. Confirm the button "View product on store" is visible.

@Hicham, if the product visibility is private, "View product on store" button becomes invisible. Is the instruction wrong?