fix(native): dedupe cold-start deep-link double navigation (D4)

on_open_url and the argv fallback can both forward the same launch matrix: URL
on cold start, navigating the room twice. forward_deeplink now drops a repeat of
the same URL within ~1s (plain std Mutex/Instant — no windows-crate surface).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src-tauri/src/lib.rs

@@ -27,6 +27,24 @@ fn show_main(app: &tauri::AppHandle) {
 /// CustomEvent the client listens for (see useDeepLinkNavigate.ts). Uses
 /// `eval` so we don't need the @tauri-apps/api event package on the web side.
 fn forward_deeplink(app: &tauri::AppHandle, url: &str) {
+    // Dedupe: on a cold start the deep-link plugin's `on_open_url` AND the argv
+    // fallback (`matrix_url_from_args(std::env::args())`) can both forward the
+    // same launch URL, navigating the room twice (re-show/re-focus + a duplicate
+    // `lotus-deeplink`). Drop a repeat of the same URL within a short window.
+    {
+        use std::sync::Mutex;
+        use std::time::{Duration, Instant};
+        static LAST: Mutex<Option<(String, Instant)>> = Mutex::new(None);
+        if let Ok(mut last) = LAST.lock() {
+            let now = Instant::now();
+            if let Some((prev_url, prev_at)) = last.as_ref() {
+                if prev_url == url && now.duration_since(*prev_at) < Duration::from_millis(1000) {
+                    return;
+                }
+            }
+            *last = Some((url.to_string(), now));
+        }
+    }
     show_main(app);
     if let Some(window) = app.get_webview_window("main") {
         if let Ok(json) = serde_json::to_string(url) {