Extract EnsureProcessRunning helper to eliminate code duplication (#44235)

## Summary of the Pull Request

Addresses code review feedback on #42642 by extracting duplicated
process launching logic into a reusable helper method.

## PR Checklist

- [ ] **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

## Detailed Description of the Pull Request / Additional comments

The `ApplyColorTemperature` and `ApplyProfile` custom action handlers
contained identical 6-line blocks for process state checking, launching,
and synchronization.

**Changes:**
- Added `EnsureProcessRunning()` helper encapsulating the pattern: check
if running → launch if needed → wait for ready signal
- Replaced duplicated blocks in both handlers with single helper call

**Before:**
```cpp
if (!is_process_running())
{
    Logger::trace(L"PowerDisplay process not running, launching before applying...");
    launch_process();
    wait_for_process_ready();
}
```

**After:**
```cpp
EnsureProcessRunning();
```

## Validation Steps Performed

Code review and security checks passed.

<!-- START COPILOT CODING AGENT TIPS -->
---

💬 We'd love your input! Share your thoughts on Copilot coding agent in
our [2 minute survey](https://gh.io/copilot-coding-agent-survey).

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: moooyo <42196638+moooyo@users.noreply.github.com>

src/modules/powerdisplay/PowerDisplayModuleInterface/dllmain.cpp

@@ -217,6 +217,18 @@ private:
         }
     }
 
+    // Helper method to ensure PowerDisplay process is running
+    // Checks if process is running, launches it if needed, and waits for ready signal
+    void EnsureProcessRunning()
+    {
+        if (!is_process_running())
+        {
+            Logger::trace(L"PowerDisplay process not running, launching");
+            launch_process();
+            wait_for_process_ready();
+        }
+    }
+
 public:
     PowerDisplayModule()
     {
@@ -360,13 +372,7 @@ public:
                 Logger::trace(L"Event name: {}", CommonSharedConstants::APPLY_COLOR_TEMPERATURE_POWER_DISPLAY_EVENT);
 
                 // Ensure PowerDisplay process is running before signaling event
-                if (!is_process_running())
-                {
-                    Logger::trace(L"PowerDisplay process not running, launching before applying color temperature");
-                    launch_process();
-                    // Wait for process to signal ready
-                    wait_for_process_ready();
-                }
+                EnsureProcessRunning();
 
                 if (m_hApplyColorTemperatureEvent)
                 {
@@ -391,13 +397,7 @@ public:
                 Logger::trace(L"ApplyProfile action received");
 
                 // Ensure PowerDisplay process is running before signaling event
-                if (!is_process_running())
-                {
-                    Logger::trace(L"PowerDisplay process not running, launching before applying profile");
-                    launch_process();
-                    // Wait for process to signal ready
-                    wait_for_process_ready();
-                }
+                EnsureProcessRunning();
 
                 if (m_hApplyProfileEvent)
                 {