feat(app): remember window size/position across restarts (window-state plugin)

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

app/src-tauri/Cargo.lock

@@ -3228,6 +3228,7 @@ dependencies = [
  "tauri",
  "tauri-build",
  "tauri-plugin-notification",
+ "tauri-plugin-window-state",
  "tokio",
 ]
 
@@ -3549,6 +3550,21 @@ dependencies = [
  "url",
 ]
 
+[[package]]
+name = "tauri-plugin-window-state"
+version = "2.4.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "73736611e14142408d15353e21e3cca2f12a3cfb523ad0ce85999b6d2ef1a704"
+dependencies = [
+ "bitflags 2.13.0",
+ "log",
+ "serde",
+ "serde_json",
+ "tauri",
+ "tauri-plugin",
+ "thiserror 2.0.18",
+]
+
 [[package]]
 name = "tauri-runtime"
 version = "2.11.2"