refactor: split remote relay into own module, add lifecycle reconnect

- Move handle_remote_relay from remote_input.rs to remote_relay.rs
- Android: lifecycle-aware WebSocket reconnection on app resume
- Cleaner module boundaries between xdotool input and browser relay

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

core/archipelago/src/api/handler/mod.rs

@@ -3,6 +3,7 @@ mod dwn;
 mod node_message;
 mod proxy;
 mod remote_input;
+mod remote_relay;
 mod websocket;
 
 use crate::api::rpc::RpcHandler;