fix(core): ai message resending (#13359)

Close [AI-395](https://linear.app/affine-design/issue/AI-395)

<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit

* **Bug Fixes**
* Improved chat stability by resetting chat action signals after
processing to prevent repeated triggers.

* **New Features**
* Added end-to-end tests for new chat session creation and chat pinning
functionality to enhance reliability.

* **Enhancements**
* Enhanced chat toolbar with test identifiers and pinned state
attributes for better accessibility and testing.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->

Co-authored-by: fengmk2 <fengmk2@gmail.com>

packages/frontend/core/src/blocksuite/ai/components/ai-chat-content/ai-chat-content.ts

@@ -391,6 +391,7 @@ export class AIChatContent extends SignalWatcher(
               })
               .catch(console.error);
           }
+          AIProvider.slots.requestOpenWithChat.next(null);
         }
       )
     );

packages/frontend/core/src/blocksuite/ai/components/ai-chat-input/ai-chat-input.ts

@@ -405,6 +405,7 @@ export class AIChatInput extends SignalWatcher(
               this.send(input).catch(console.error);
             }, 0);
           }
+          AIProvider.slots.requestSendWithChat.next(null);
         }
       )
     );

packages/frontend/core/src/blocksuite/ai/components/ai-chat-toolbar/ai-chat-toolbar.ts

@@ -92,14 +92,20 @@ export class AIChatToolbar extends WithDisposable(ShadowlessElement) {
     const pinned = this.session?.pinned;
     return html`
       <div class="ai-chat-toolbar">
-        <div class="chat-toolbar-icon" @click=${this.onPlusClick}>
+        <div
+          class="chat-toolbar-icon"
+          @click=${this.onPlusClick}
+          data-testid="ai-panel-new-chat"
+        >
           ${PlusIcon()}
           <affine-tooltip>New Chat</affine-tooltip>
         </div>
         <div
           class="chat-toolbar-icon"
           @click=${this.onPinClick}
+          data-pinned=${!!pinned}
           data-disabled=${this.isGenerating}
+          data-testid="ai-panel-pin-chat"
         >
           ${pinned ? PinedIcon() : PinIcon()}
           <affine-tooltip>