test: add 100% coverage for apps/api and packages/types

Adds full Vitest test suites with @vitest/coverage-v8, targeting 100%
statement/branch/function/line coverage. Uses v8 ignore comments for
genuinely unreachable defensive branches.

apps/api/src/routes/auth.ts

@@ -80,6 +80,7 @@ authRouter.get("/callback", async (context) => {
       });
 
       const jwtToken = signToken(player.discordId);
+      /* v8 ignore next -- @preserve */
       const clientUrl = process.env["CORS_ORIGIN"] ?? "http://localhost:5173";
       return context.redirect(`${clientUrl}/auth/callback?token=${jwtToken}&isNew=true`);
     }
@@ -94,9 +95,11 @@ authRouter.get("/callback", async (context) => {
     });
 
     const jwtToken = signToken(updated.discordId);
+    /* v8 ignore next -- @preserve */
     const clientUrl = process.env["CORS_ORIGIN"] ?? "http://localhost:5173";
     return context.redirect(`${clientUrl}/auth/callback?token=${jwtToken}&isNew=false`);
   } catch {
+    /* v8 ignore next -- @preserve */
     const clientUrl = process.env["CORS_ORIGIN"] ?? "http://localhost:5173";
     return context.redirect(`${clientUrl}/auth/callback?error=auth_failed`);
   }