Implement consistent logging across the application

[conico974]

Introduce a centralized logging mechanism to ensure uniform logging practices throughout the app. Move the logger initialization to a dedicated file and utilize the logger in various components for improved traceability and debugging.

We will have the same requestId between the middleware and the server function.

It also remove a lot of logs that were not useful.

[linear]

RND-7359 Create a custom logger for GBO

[changeset-bot]

⚠️ No Changeset found

Latest commit: d1cf1f6

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[github-actions]

Summary of the deployments:

Version	URL	Status
Vercel	https://gitbook-v2-6evvojj2b-gitbook.vercel.app	✅
Cloudflare	https://144434a0-gitbook-open-v2-preview.gitbook.workers.dev	✅

Test content

Site	2v	2c
GitBook	https://gitbook-v2-6evvojj2b-gitbook.vercel.app/url/gitbook.com/docs	https://144434a0-gitbook-open-v2-preview.gitbook.workers.dev/url/gitbook.com/docs
E2E	https://gitbook-v2-6evvojj2b-gitbook.vercel.app/url/gitbook.gitbook.io/test-gitbook-open	https://144434a0-gitbook-open-v2-preview.gitbook.workers.dev/url/gitbook.gitbook.io/test-gitbook-open

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Build	Status	Details	Updated (UTC)
customers-v2 (Inspect)	✅ No changes detected	-	Jul 10, 2025, 2:31 PM
v2-cloudflare (Inspect)	👍 Changes approved	1 changed	Jul 10, 2025, 2:36 PM
v2-vercel (Inspect)	👍 Changes approved	1 changed	Jul 10, 2025, 2:33 PM