[codex] add competition setup flow before starting a game

[troccoli]

Summary

This branch introduces a proper pre-game setup flow and standardises the domain language around competition.

What changed

• added a dedicated Livewire Competition component and /competition page for creating competition details
• updated the setup flow so incomplete setup redirects to /setup before a user can reach /game
• reworked the setup screen to show setup progress, allow inline competition editing, and improve the introductory guidance
• replaced remaining championship terminology across code, relationships, labels, variables, and schema references with competition
• adjusted the setup UI to use a light presentation and avoid overriding Flux heading/text colours
• added and updated feature coverage for competition and setup routing behaviour

Why

Issue #16 required the single-game flow to include a real setup experience before a game can start. The branch also removes the mixed championship/competition terminology that was leaking through the codebase and UI.

Impact

Users are now guided through the required setup steps before starting a game, can create and edit the competition inline during setup, and see consistent competition terminology throughout the application.

Validation

• php artisan test --compact tests/Feature/CompetitionPageTest.php
• php artisan test --compact tests/Feature/MatchSetupRoutingTest.php
• php ./vendor/bin/phpstan analyse app/ database/factories/ database/seeders/ --memory-limit=2G --debug
• vendor/bin/pint --dirty --format agent
• vendor/bin/rector process --clear-cache --memory-limit=2G

Closes #16