Refactor tournament submission to use the otr-api-client

[myssto]

Closes #222

Models how I would go about refactoring the site to use the new client package starting with the tournament submission form. Everything related is now 100% type safe and refactorable.

Changes:

• Refactor the locations of some components to be more consistent
• Start abstracting some of the content in @/lib to improve readability
• Rearrange some of the fields on the tournament submission form
• Improve the error detail for malformed form submissions
• Add a form field for submitting beatmap ids

Changes that still need to be done:

• Allow admins to submit with no mp links
• Allow admins to submit with a rejection reason
  • Investigate usage of bitwise enums in zod / in the codebase in general
• Improve the info icon text for the mp and beatmap links fields

[AkinariHex]

The Changes that still need to be done will be done here or later in the future?