feat: add background sync for Matrix client on mobile platforms

- Introduced background sync functionality for the Matrix client, allowing notifications to be received even when the app is backgrounded.
- Added new commands to start, stop, and get the state of background sync.
- Implemented a BackgroundSyncManager to manage sync state and credentials.
- Integrated matrix-sdk for handling Matrix interactions and notifications.
- Updated Cargo.toml to include necessary dependencies for background sync.
- Modified mobile capabilities to include opener permissions.
- Enhanced lib.rs to handle new commands and integrate background sync logic.

src-tauri/Cargo.toml

@@ -24,6 +24,7 @@ serde = { version = "1.0", features = ["derive"] }
 tauri = { version = "2", features = ["devtools", "tray-icon", "image-png"] }
 tauri-plugin-opener = "2"
 tauri-plugin-notification = "2"
+log = "0.4"
 
 [target."cfg(target_os = \"linux\")".dependencies]
 arboard = { version = "3", features = ["wayland-data-control"] }
@@ -35,6 +36,10 @@ gtk = "0.18"
 [target."cfg(any(target_os = \"android\", target_os = \"ios\"))".dependencies]
 tauri-plugin-deep-link = "2"
 
+# Matrix SDK for native background sync (no sqlite on mobile - use in-memory store)
+matrix-sdk = { version = "0.7", default-features = false, features = ["rustls-tls", "e2e-encryption"] }
+tokio = { version = "1", features = ["rt-multi-thread", "sync", "time"] }
+
 [target."cfg(not(any(target_os = \"android\", target_os = \"ios\")))".dependencies]
 tauri-plugin-localhost = "2"
 tauri-plugin-window-state = "2"