chore: migrate api/availability/calendar to App Router

[hbjORbj]

What does this PR do?

• Migrates /api/availability/calendar.ts to App Router

Tested

POST

DELETE

Mandatory Tasks (DO NOT REMOVE)

• I have self-reviewed the code (A decent size PR without self-review might be rejected).
• N/A - 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?

• Go to /apps/installed/calendar and toggle on/off the calendars (inspect the Network tab to see /api/availability/calendar request)

[vercel]

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[graphite-app]

Graphite Automations

"Add consumer team as reviewer" took an action on this PR • (02/04/25)

1 reviewer was added to this PR based on Keith Williams's automation.

"Add foundation team as reviewer" took an action on this PR • (02/04/25)

1 reviewer was added to this PR based on Keith Williams's automation.

[github-actions]

E2E results are ready!

• Workflow #46359.1 latest results