feat: move router to app dir

[sean-brydon]

What does this PR do?

• Fixes #XXXX (GitHub issue number)
• Fixes CAL-XXXX (Linear issue number - should be visible at the bottom of the GitHub issue description)

Visual Demo (For contributors especially)

A visual demonstration is strongly recommended, for both the original and new change (video / image - any one).

Video Demo (if applicable):

• Show screen recordings of the issue or feature.
• Demonstrate how to reproduce the issue, the behavior before and after the change.

Image Demo (if applicable):

• Add side-by-side screenshots of the original and updated change.
• Highlight any significant change(s).

Mandatory Tasks (DO NOT REMOVE)

• I have self-reviewed the code (A decent size PR without self-review might be rejected).
• I have updated the developer docs in /docs if this PR makes changes that would require a documentation change. If N/A, write N/A here and check the checkbox.
• I confirm automated tests are in place that prove my fix is effective or that my feature works.

How should this be tested?

• Are there environment variables that should be set?
• What are the minimal test data to have?
• What is expected (happy path) to have (input and output)?
• Any other important info that could help to test that PR

Checklist

• I haven't read the contributing guide
• My code doesn't follow the style guidelines of this project
• I haven't commented my code, particularly in hard-to-understand areas
• I haven't checked if my changes generate no new warnings

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2 Skipped Deployments

Name	Status	Preview	Comments	Updated (UTC)
cal	⬜️ Ignored (Inspect)			Feb 25, 2025 2:59pm
calcom-web-canary	⬜️ Ignored (Inspect)			Feb 25, 2025 2:59pm

[sean-brydon]

Cache this call so we dont need to refetch this data in the title and loading the page

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🚮 Removed packages: npm/@formkit/[email protected]

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