chore: Improve Error Handling in API Routes

[SujalTripathi]

Description

The existing API routes (/api/bookings, /api/instructors) have minimal
or no error handling. Missing validation and unstructured error responses
make debugging difficult and expose the API to bad inputs.

Current Behavior

• No input validation on POST /api/bookings
• Generic or no error responses returned
• No HTTP status codes used correctly
• No handling for missing required fields

Expected Behavior

• All required fields validated before processing
• Correct HTTP status codes: 400 (bad input), 404 (not found), 500 (server error)
• Structured JSON error responses: { error: "message" }
• Try/catch blocks around all async operations

Acceptance Criteria

• Input validation added to POST /api/bookings
• Correct status codes returned
• Structured { error: "..." } JSON responses
• Try/catch on all async API handlers
• Missing field errors return 400 with field name

Contributing on behalf of NSoC'26 | @Mehren7 please assign me

[omkartike]

i would like to work on this issue under nsoc , i think the previous assignee is not doing anything , so is it possible that i can work on this ??

[SujalTripathi]

@omkartike bhai mai kaam kar hi raha hu but first maintainer PR toh merge kare mera open hai voh hi inactive hai toh mai kya karu