Use Qt 6.5 setBadgeNumber on Server

**What is the current behaviour and why should it be changed?**
Currently we're not using the Qt 6.5 but the native Objective C code to set the Badge on macOS. Once we've moved to Qt6.5 we should add a conditional compilation step to use setBadgeNumber: https://doc-snapshots.qt.io/qt6-dev/qguiapplication.html#setBadgeNumber

**Describe possible approaches**
* Remove the objective C code fully (breaks compatibility; I think that's too early)
* Keep the old logic

**Has this feature been discussed and generally agreed?**
No

Review the existing native Objective-C badge logic and the Qt 6.5 QGuiApplication::setBadgeNumber documentation. Clarify whether the Qt path should be conditionally used while preserving compatibility with older Qt versions, then verify that macOS badge behavior remains correct.

Written by the indexing model from the issue text.