feat(arayüz): API istemcisi, TanStack Query, ts-rs tip üretimi ve oturum durumu

- Backend: ts-rs ile DTO'lardan TypeScript tipleri (frontend/src/types, npm run types)
- Hata ve health yanıtları tipli yapılara çevrildi
- lib/api.ts: tek API istemcisi, Türkçe ApiError, ağ hatası mesajı
- lib/query.ts: QueryClient (4xx tekrar denenmez, 401 → oturum kapanır)
- lib/auth.ts: useMe, useLogin, useRegister, useLogout
- Vitest: 7 API istemcisi testi (toplam 29)

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

backend/Cargo.lock

@@ -1298,6 +1298,7 @@ dependencies = [
  "tower",
  "tracing",
  "tracing-subscriber",
+ "ts-rs",
  "uuid",
  "validator",
 ]
@@ -2429,6 +2430,15 @@ version = "1.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "55937e1799185b12863d447f42597ed69d9928686b8d88a1df17376a097d8369"
 
+[[package]]
+name = "termcolor"
+version = "1.4.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "06794f8f6c5c898b3275aebefa6b8a1cb24cd2c6c79397ab15774837a0bc5755"
+dependencies = [
+ "winapi-util",
+]
+
 [[package]]
 name = "thiserror"
 version = "2.0.21"
@@ -2656,6 +2666,28 @@ dependencies = [
  "tracing-log",
 ]
 
+[[package]]
+name = "ts-rs"
+version = "12.0.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "756050066659291d47a554a9f558125db17428b073c5ffce1daf5dcb0f7231d8"
+dependencies = [
+ "thiserror",
+ "ts-rs-macros",
+]
+
+[[package]]
+name = "ts-rs-macros"
+version = "12.0.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "38d90eea51bc7988ef9e674bf80a85ba6804739e535e9cab48e4bb34a8b652aa"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "syn 2.0.119",
+ "termcolor",
+]
+
 [[package]]
 name = "typed-builder"
 version = "0.22.0"