Use proper clipboard writing method

src-tauri/Cargo.toml

@@ -16,3 +16,4 @@ tauri-build = { version = "2.5.5", features = [] }
 tauri = { version = "2.10.2", features = [] }
 serde = { version = "1.0.228", features = ["derive"] }
 serde_json = "1.0.149"
+tauri-plugin-clipboard-manager = "2.3.2"