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, 6 deletions

diff --git a/backend/gen/api/handler_wrapper_gen.go b/backend/gen/api/handler_wrapper_gen.go
index 5a5ce2d..c6e3e8a 100644
--- a/backend/gen/api/handler_wrapper_gen.go
+++ b/backend/gen/api/handler_wrapper_gen.go
@@ -131,17 +131,13 @@ func NewHandler(queries *db.Queries, hub GameHubInterface, conf *config.Config)
 			user, ok := GetJWTClaimsFromContext(ctx)
 			if !ok {
 				return {{ .Name }}401JSONResponse{
-					UnauthorizedJSONResponse: UnauthorizedJSONResponse{
-						Message: "Unauthorized",
-					},
+					Message: "Unauthorized",
 				}, nil
 			}
 			{{ if .RequiresAdminRole -}}
 				if !user.IsAdmin {
 					return {{ .Name }}403JSONResponse{
-						ForbiddenJSONResponse: ForbiddenJSONResponse{
-							Message: "Forbidden",
-						},
+						Message: "Forbidden",
 					}, nil
 				}
 			{{ end -}}