studio: sync compare-composer reasoning state and harden compare id

- Compare composer: keep "Preserve thinking" consistent with reasoning,
  matching the main composer. Enabling it now turns reasoning on, and
  disabling reasoning (the None option or the Thinking toggle) turns it
  off, so the invalid "preserve on while thinking off" state can't occur.
- Guard crypto.randomUUID in the Compare action. It is undefined in
  non-secure contexts (HTTP over a LAN IP) and would throw; fall back to
  a timestamped random id, matching createNavigationNonce.

studio/frontend/src/components/assistant-ui/thread.tsx

@@ -1315,7 +1315,12 @@ const ComposerToolsMenu: FC<{ side?: "top" | "bottom" }> = ({
     const store = useChatRuntimeStore.getState();
     store.setActiveThreadId(null);
     store.setContextUsage(null);
-    navigate({ to: "/chat", search: { compare: crypto.randomUUID() } });
+    // crypto.randomUUID is undefined in non-secure contexts (HTTP over a LAN IP).
+    const compareId =
+      typeof globalThis.crypto?.randomUUID === "function"
+        ? globalThis.crypto.randomUUID()
+        : `${Date.now()}-${Math.random().toString(36).slice(2, 10)}`;
+    navigate({ to: "/chat", search: { compare: compareId } });
   }, [navigate]);
 
   return (

studio/frontend/src/features/chat/shared-composer.tsx

@@ -1038,6 +1038,8 @@ export function SharedComposer({
                           onSelect={() => {
                             setReasoningEnabled(false);
                             applyQwenThinkingParams(false);
+                            // Preserve thinking needs thinking on, so turn it off too.
+                            setPreserveThinking(false);
                           }}
                         >
                           <CheckIcon
@@ -1093,6 +1095,8 @@ export function SharedComposer({
                           const next = !reasoningEnabled;
                           setReasoningEnabled(next);
                           applyQwenThinkingParams(next);
+                          // Preserve thinking cannot run without thinking.
+                          if (!next) setPreserveThinking(false);
                           if (isKimiExternal && next && toolsEnabled) {
                             setToolsEnabled(false, { persist: false });
                           }
@@ -1113,7 +1117,13 @@ export function SharedComposer({
                       disabled={!modelLoaded}
                       onSelect={(e) => {
                         e.preventDefault();
-                        setPreserveThinking(!preserveThinking);
+                        const next = !preserveThinking;
+                        setPreserveThinking(next);
+                        // Preserve thinking requires thinking on.
+                        if (next) {
+                          setReasoningEnabled(true);
+                          applyQwenThinkingParams(true);
+                        }
                       }}
                     >
                       <CheckIcon