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>

2 files changed, 53 insertions, 0 deletions

diff --git a/typespec/fortee/main.tsp b/typespec/fortee/main.tsp
new file mode 100644
index 0000000..03683a7
--- /dev/null
+++ b/typespec/fortee/main.tsp
@@ -0,0 +1,45 @@
+import "@typespec/http";
+import "@typespec/openapi";
+import "@typespec/openapi3";
+
+using TypeSpec.Http;
+using TypeSpec.OpenAPI;
+
+@service(#{
+  title: "fortee API",
+})
+@info(#{
+  version: "0.1.0",
+})
+namespace ForteeApi;
+
+@route("/api/user/login")
+@post
+@operationId("postLogin")
+op postLogin(
+  @header contentType: "application/x-www-form-urlencoded",
+  @body body: {
+    username: string;
+    password: string;
+  },
+): {
+  @body body: {
+    loggedIn: boolean;
+    user?: {
+      username: string;
+    };
+  };
+};
+
+@route("/api/user/view/{username}")
+@get
+@operationId("getUser")
+op getUser(@path username: string): {
+  @body body: {
+    uuid: string;
+    username: string;
+    avatar_url: string;
+  };
+} | {
+  @statusCode statusCode: 404;
+};
diff --git a/typespec/fortee/tspconfig.yaml b/typespec/fortee/tspconfig.yaml
new file mode 100644
index 0000000..78ba744
--- /dev/null
+++ b/typespec/fortee/tspconfig.yaml
@@ -0,0 +1,8 @@
+output-dir: "{project-root}/tsp-output"
+emit:
+  - "@typespec/openapi3"
+options:
+  "@typespec/openapi3":
+    openapi-versions:
+      - "3.0.0"
+    output-file: openapi.yaml