feat(openapi): generate OpenAPI specs from TypeSpec sources

Migrate hand-written OpenAPI YAML to TypeSpec (.tsp) source files.
TypeSpec compiles to OpenAPI 3.0 YAML, enabling type-safe API definitions.

- Add typespec/ directory with api-server and fortee definitions
- Integrate TypeSpec build into `just gen` and `just build` pipelines
- Update backend handler code to match new generated type names
  (inlined error responses, separate GameType/ProblemLanguage enums)
- Regenerate frontend TypeScript types from new OpenAPI output

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

1 files changed, 2 insertions, 0 deletions

diff --git a/justfile b/justfile
index de2a8fa..4c621f6 100644
--- a/justfile
+++ b/justfile
@@ -4,6 +4,7 @@ default: down build up
 
 build:
     {{ docker_compose }} build
+    cd typespec; npm install
     cd frontend; npm install
 
 up:
@@ -48,6 +49,7 @@ initdb:
     just psql-query < ./backend/fixtures/dev.sql
 
 gen:
+    cd typespec; npm run build
     cd backend; just gen
     cd frontend; npm run openapi-typescript