Cmdpal extension: Powertoys extension for cmdpal (#44006)

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fix/what does it change/how was it tested (even manually, if necessary)?
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## Summary of the Pull Request

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## PR Checklist

- [ ] Closes: #xxx
<!-- - [ ] Closes: #yyy (add separate lines for additional resolved
issues) -->
- [ ] **Communication:** I've discussed this with core contributors
already. If the work hasn't been agreed, this work might be rejected
- [ ] **Tests:** Added/updated and all pass
- [ ] **Localization:** All end-user-facing strings can be localized
- [ ] **Dev docs:** Added/updated
- [ ] **New binaries:** Added on the required places
- [ ] [JSON for
signing](https://github.com/microsoft/PowerToys/blob/main/.pipelines/ESRPSigning_core.json)
for new binaries
- [ ] [WXS for
installer](https://github.com/microsoft/PowerToys/blob/main/installer/PowerToysSetup/Product.wxs)
for new binaries and localization folder
- [ ] [YML for CI
pipeline](https://github.com/microsoft/PowerToys/blob/main/.pipelines/ci/templates/build-powertoys-steps.yml)
for new test projects
- [ ] [YML for signed
pipeline](https://github.com/microsoft/PowerToys/blob/main/.pipelines/release.yml)
- [ ] **Documentation updated:** If checked, please file a pull request
on [our docs
repo](https://github.com/MicrosoftDocs/windows-uwp/tree/docs/hub/powertoys)
and link it here: #xxx

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or any additional comments/features here -->
## Detailed Description of the Pull Request / Additional comments

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## Validation Steps Performed
Installer built, and every command works as expected,
Now use sparse app deployment, so we don't need an extra msix

---------

Co-authored-by: kaitao-ms <kaitao1105@gmail.com>

src/modules/AdvancedPaste/AdvancedPasteModuleInterface/dllmain.cpp

@@ -15,9 +15,11 @@
 #include <common/utils/logger_helper.h>
 #include <common/utils/winapi_error.h>
 #include <common/utils/gpo.h>
+#include <common/utils/EventWaiter.h>
 
 #include <algorithm>
 #include <cwctype>
+#include <thread>
 #include <vector>
 
 BOOL APIENTRY DllMain(HMODULE /*hModule*/, DWORD ul_reason_for_call, LPVOID /*lpReserved*/)
@@ -101,6 +103,9 @@ private:
     bool m_is_advanced_ai_enabled = false;
     bool m_preview_custom_format_output = true;
 
+    // Event listening for external triggers (e.g., from CmdPal extension)
+    EventWaiter m_triggerEventWaiter;
+
     Hotkey parse_single_hotkey(const wchar_t* keyName, const winrt::Windows::Data::Json::JsonObject& settingsObject)
     {
         try
@@ -779,6 +784,17 @@ public:
         Trace::AdvancedPaste_Enable(true);
         m_enabled = true;
         m_process_manager.start();
+
+        // Start listening for external trigger event so we can invoke the same logic as the hotkey.
+        // Note: Use start() directly instead of constructor + move assignment to avoid dangling this pointer in the thread.
+        m_triggerEventWaiter.start(CommonSharedConstants::ADVANCED_PASTE_SHOW_UI_EVENT, [this](DWORD) {
+            // Same logic as hotkeyId == 1 (m_advanced_paste_ui_hotkey)
+            Logger::trace(L"AdvancedPaste ShowUI event triggered");
+            m_process_manager.start();
+            m_process_manager.bring_to_front();
+            m_process_manager.send_message(CommonSharedConstants::ADVANCED_PASTE_SHOW_UI_MESSAGE);
+            Trace::AdvancedPaste_Invoked(L"AdvancedPasteUIEvent");
+        });
     };
 
     void Disable(bool traceEvent)
@@ -787,6 +803,9 @@ public:
         {
             m_process_manager.stop();
 
+            // Stop event listening
+            m_triggerEventWaiter.stop();
+
             if (traceEvent)
             {
                 Trace::AdvancedPaste_Enable(false);