Fix page group not expanded by default

[gregberge]

When the page is the root, the path is "". To test if a page is a
children of this one we have to test all possible paths of the page.

[linear]

RND-4525 Page groups are not expanded by default in published content

[changeset-bot]

🦋 Changeset detected

Latest commit: 11e2fab

The changes in this PR will be included in the next version bump.

This PR includes changesets to release 1 package

Name	Type
gitbook	Patch

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[github-actions]

Summary of the deployments:

Version 1

Version	URL	Status
Latest commit	https://992c8bb7.gitbook-open.pages.dev	✅
PR	https://pr3358.gitbook-open.pages.dev	✅

Version 2

Version	URL	Status
Vercel	https://gitbook-v2-4pomafris-gitbook.vercel.app	✅
Cloudflare	https://1be22ea7-gitbook-open-v2-preview.gitbook.workers.dev	✅

Test content

Site	v1	2v	2c
GitBook	https://992c8bb7.gitbook-open.pages.dev/gitbook.com/docs	https://gitbook-v2-4pomafris-gitbook.vercel.app/url/gitbook.com/docs	https://1be22ea7-gitbook-open-v2-preview.gitbook.workers.dev/url/gitbook.com/docs
E2E	https://992c8bb7.gitbook-open.pages.dev/gitbook.gitbook.io/test-gitbook-open	https://gitbook-v2-4pomafris-gitbook.vercel.app/url/gitbook.gitbook.io/test-gitbook-open	https://1be22ea7-gitbook-open-v2-preview.gitbook.workers.dev/url/gitbook.gitbook.io/test-gitbook-open

[argos-ci]

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Build	Status	Details	Updated (UTC)
customers-v1 (Inspect)	✅ No changes detected	-	Jun 19, 2025, 11:58 AM
customers-v2 (Inspect)	👍 Changes approved	74 changed	Jun 19, 2025, 11:59 AM
default (Inspect)	✅ No changes detected	-	Jun 19, 2025, 12:01 PM
v2-cloudflare (Inspect)	👍 Changes approved	1 changed	Jun 19, 2025, 12:01 PM
v2-vercel (Inspect)	👍 Changes approved	1 changed	Jun 19, 2025, 12:25 PM

[conico974]

I don't think there will be too many instance of this one. But if it starts to become a problem, we'll have to consider passing less data to it