Merged PR 48958: Mark release builds as "stable"

#### AI description  (iteration 1)
#### PR Classification
New feature

#### PR Summary
This pull request marks release builds as "stable" by setting the `DotNetFinalVersionKind` property to "release".
- `eng/Versions.props`: Added `DotNetFinalVersionKind` property to mark builds as stable for release branches.
- `eng/MSBuild/ProjectStaging.props`: Removed redundant setting of `DotNetFinalVersionKind` property.
<!-- GitOpsUserAgent=GitOps.Apps.Server.pullrequestcopilot -->

Author: RussKie

eng/MSBuild/ProjectStaging.props

@@ -11,12 +11,6 @@
       -->
     <_IsStable Condition="('$(Stage)' != 'dev' and '$(Stage)' != 'preview') Or '$(MSBuildProjectName)' == 'Microsoft.AspNetCore.Testing'">true</_IsStable>
 
-    <!--
-        When DotNetFinalVersionKind is set to 'release' (only for the release branches),
-        the build will produce stable outputs for 'Shipping' packages.
-      -->
-    <DotNetFinalVersionKind Condition=" '$(StabilizePackageVersion)' == 'true' And '$(DotNetFinalVersionKind)' == '' And '$(_IsStable)' == 'true' ">release</DotNetFinalVersionKind>
-
     <!-- Preview packages: do not use stable branding and do not warn about lack of [Experimental] -->
     <NoWarn Condition="'$(Stage)' == 'dev' or '$(Stage)' == 'preview'">$(NoWarn);LA0003</NoWarn>
     <!--

eng/Versions.props

@@ -12,6 +12,15 @@
         When StabilizePackageVersion is set to 'true', this branch will produce stable outputs for 'Shipping' packages
     -->
     <StabilizePackageVersion Condition="'$(StabilizePackageVersion)' == ''">true</StabilizePackageVersion>
+
+    <!--
+        When DotNetFinalVersionKind is set to 'release' (only for the release branches),
+        the build will produce stable outputs for 'Shipping' packages.
+
+        This is used by the Arcade SDK (Publish.proj) to determine if the build is a release build or not.
+      -->
+    <DotNetFinalVersionKind>release</DotNetFinalVersionKind>
+
     <!-- Enabling this rule will cause build failures on undocumented public APIs. -->
     <SkipArcadeNoWarnCS1591>true</SkipArcadeNoWarnCS1591>
   </PropertyGroup>