Unify api validations and setup consistent prettier formatting

[aahnik]

This pull request includes several changes to improve code formatting, update import paths, and ensure consistent coding standards. The most important changes include adding a Prettier configuration, setting up a GitHub workflow to check formatting, updating import paths for validation schemas, and applying consistent code formatting across various files.

Code Formatting and Configuration:

• Added a Prettier configuration file to enforce consistent code formatting rules (.prettierrc). (,prettierrcR1-R22)
• Created a GitHub Actions workflow to check Prettier formatting on push and pull request events to the main branch (.github/workflows/format.yml).
• Added a .prettierignore file to exclude certain directories from Prettier formatting (.prettierignore).

Import Path Updates:

• Updated import paths for validation schemas to use the centralized @/lib/validations module across various API route files. (app/api/orgs/[orgId]/contests/[contestId]/participants/route.tsL3-R3, app/api/orgs/[orgId]/contests/route.tsL7-R7, app/api/orgs/[orgId]/groups/[groupId]/members/route.tsL3-R3, app/api/orgs/[orgId]/groups/route.tsL3-R3, app/api/orgs/[orgId]/groups/service.tsL5-R5, app/api/orgs/[orgId]/problems/[problemId]/test-cases/route.tsL2-R2, app/api/orgs/[orgId]/problems/route.tsL1-R1, app/api/users/[userId]/route.tsL1-R1, app/api/users/route.tsL2-R2, app/api/orgs/[orgId]/problems/service.tsL4-R4)

Consistent Code Formatting:

• Applied consistent code formatting to various TypeScript and JavaScript files, ensuring proper use of semicolons, single quotes, and other style rules. [1] [2] app/contest/[id]/page.tsxL1-L6, [3] [4] [5] [6]