fix: split view focus (#11217)

# After:

https://github.com/user-attachments/assets/990d500d-2da7-488e-ac32-dd7bd229f896

# Before:

https://github.com/user-attachments/assets/6676766a-c76a-414b-a35e-53d2cda10c24

blocksuite/framework/block-std/src/event/dispatcher.ts

@@ -1,5 +1,6 @@
 import { DisposableGroup } from '@blocksuite/global/disposable';
 import { BlockSuiteError, ErrorCode } from '@blocksuite/global/exceptions';
+import { signal } from '@preact/signals-core';
 
 import { LifeCycleWatcher } from '../extension/index.js';
 import { KeymapIdentifier } from '../identifier.js';
@@ -81,7 +82,7 @@ export class UIEventDispatcher extends LifeCycleWatcher {
 
   static override readonly key = 'UIEventDispatcher';
 
-  private _active = false;
+  private readonly _active = signal(false);
 
   private readonly _clipboardControl: ClipboardControl;
 
@@ -105,6 +106,10 @@ export class UIEventDispatcher extends LifeCycleWatcher {
   }
 
   get active() {
+    return this._active.peek();
+  }
+
+  get active$() {
     return this._active;
   }
 
@@ -302,19 +307,24 @@ export class UIEventDispatcher extends LifeCycleWatcher {
     if (active) {
       if (UIEventDispatcher._activeDispatcher !== this) {
         if (UIEventDispatcher._activeDispatcher) {
-          UIEventDispatcher._activeDispatcher._active = false;
+          UIEventDispatcher._activeDispatcher._active.value = false;
         }
         UIEventDispatcher._activeDispatcher = this;
       }
-      this._active = true;
+      this._active.value = true;
     } else {
       if (UIEventDispatcher._activeDispatcher === this) {
         UIEventDispatcher._activeDispatcher = null;
       }
-      this._active = false;
+      this._active.value = false;
     }
   }
 
+  set active(active: boolean) {
+    if (active === this._active.peek()) return;
+    this._setActive(active);
+  }
+
   add(name: EventName, handler: UIEventHandler, options?: EventOptions) {
     const runner: EventHandlerRunner = {
       fn: handler,

blocksuite/framework/block-std/src/inline/range/range-binding.ts

@@ -169,7 +169,10 @@ export class RangeBinding {
   private readonly _onNativeSelectionChanged = async () => {
     if (this.isComposing) return;
     if (!this.host) return; // Unstable when switching views, card <-> embed
-    if (!isActiveInEditor(this.host)) return;
+    if (!isActiveInEditor(this.host)) {
+      this._prevTextSelection = null;
+      return;
+    }
 
     await this.host.updateComplete;
 
@@ -251,6 +254,8 @@ export class RangeBinding {
     // TODO(@mirone): this is a trade-off, we need to use separate awareness store for every store to make sure the selection is isolated.
     const closestHost = document.activeElement?.closest('editor-host');
     if (closestHost && closestHost !== this.host) return;
+    const active = this.host.event.active;
+    if (!active) return;
 
     const text =
       selections.find((selection): selection is TextSelection =>
@@ -266,7 +271,7 @@ export class RangeBinding {
         const id = text?.blockId;
         const path = id && this._computePath(id);
 
-        if (this.host.event.active) {
+        if (active) {
           const eq =
             text && this._prevTextSelection && path
               ? text.equals(this._prevTextSelection.selection) &&