Mouse Without Borders: A conflict machine Id will make connection fail (#42190)

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fix/what does it change/how was it tested (even manually, if necessary)?
-->
## Summary of the Pull Request
This PR fixes a critical issue in Mouse Without Borders where
conflicting machine IDs would cause connection failures. The changes
ensure that when machine IDs are generated or updated, the settings are
immediately persisted to prevent loss of the new ID and maintain proper
synchronization between the property and backing field.

Key changes:

* Immediate settings persistence when a new machine ID is generated
(unless instant saving is paused)
* Proper synchronization of the machineId field when the MachineId
property is set
* Addition of settings saving logic in both getter and setter scenarios


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## PR Checklist

- [ ] Closes: #42084
- [ ] **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

<!-- Describe how you validated the behavior. Add automated tests
wherever possible, but list manual validation steps taken as well -->
## Validation Steps Performed
* Do a release bundle build and install new bundle with this fix on both
two machines
* Manually change two pc's machine ID to the same value
* Make sure they can connect
* Verify there is log entrance indicating that there is conflict for
machineID
* Close MWB, make sure next launch still connect

src/modules/MouseWithoutBorders/App/Class/Setting.cs

@@ -1055,8 +1055,13 @@ namespace MouseWithoutBorders.Class
 
                     if (machineId == 0)
                     {
-                        _properties.MachineID.Value = Common.Ran.Next();
-                        machineId = _properties.MachineID.Value;
+                        var newMachineId = Common.Ran.Next();
+                        _properties.MachineID.Value = newMachineId;
+                        machineId = newMachineId;
+                        if (!PauseInstantSaving)
+                        {
+                            SaveSettings();
+                        }
                     }
                 }
 
@@ -1068,6 +1073,11 @@ namespace MouseWithoutBorders.Class
                 lock (_loadingSettingsLock)
                 {
                     _properties.MachineID.Value = value;
+                    machineId = value;
+                    if (!PauseInstantSaving)
+                    {
+                        SaveSettings();
+                    }
                 }
             }
         }