feat: Authenticate GutenbergKit WebView requests for private sites

[dcalhoun]

Description

Provide GutenbergKit authentication cookies to allow loading protected resources
for private WordPress.com sites.

Testing instructions

1. Open the editor for a private WordPress.com site.
2. Insert various media.
3. Verify the media displays/functions as expected.

[dangermattic]

	1 Message
📖	This PR is still a Draft: some checks will be skipped.

Generated by 🚫 Danger

[sonarqubecloud]

Quality Gate passed

Issues
7 New issues
0 Accepted issues

Measures
0 Security Hotspots
0.0% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube Cloud

[wpmobilebot]

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

	App Name	WordPress
	Configuration	Release-Alpha
	Build Number	28176
	Version	PR #24669
	Bundle ID	org.wordpress.alpha
	Commit	353620d
	Installation URL	47j7nbt90ean8

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

[wpmobilebot]

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

	App Name	Jetpack
	Configuration	Release-Alpha
	Build Number	28176
	Version	PR #24669
	Bundle ID	com.jetpack.alpha
	Commit	353620d
	Installation URL	0gg4vm6fh37q8

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

[dcalhoun]

This implementation is to simple. It does not work for Atomic sites, nor does it manage expiring cookies.

Superseded by #24680, which relies on a more robust implementation that follows the existing RequestAuthenticator pattern and addresses Atomic site support and cookie expiration.