fix: Append -root to synthetic root

**Problem**
I notice that the synthetic root project ends up conflicting with
the projectMatrix on Scala 3, when the name of the matrix
matches the directory name, which is fairly common.

Also when the matrix is located at the root, we still want
the synthetic root for aggregation purpose, but we don't want
the root to end up capturing the source files.

**Solution**
1. Append `-root` to the root project.
2. Blank out the source files.

main/src/main/scala/sbt/internal/BuildDef.scala

@@ -10,13 +10,22 @@ package sbt
 package internal
 
 import java.io.File
-import Keys.{ organization, thisProject, autoGeneratedProject, publish, publishLocal, skip }
+import Keys.{
+  organization,
+  thisProject,
+  autoGeneratedProject,
+  publish,
+  publishLocal,
+  skip,
+  sources,
+}
 import Def.Setting
 // import sbt.ProjectExtra.apply
 import sbt.io.Hash
 import sbt.internal.util.{ Attributed, StringAttributeMap }
 import sbt.internal.inc.{ FileAnalysisStore, ReflectUtilities }
-import sbt.SlashSyntax0.*
+import sbt.librarymanagement.Configurations.{ Compile, Test }
+import sbt.SlashSyntax0.given
 import xsbti.{ FileConverter, VirtualFileRef }
 import xsbti.compile.CompileAnalysis
 
@@ -67,6 +76,8 @@ private[sbt] object BuildDef:
         defaultProjectSettings,
         publish / skip := true,
         publishLocal / skip := true,
+        Compile / sources := Nil,
+        Test / sources := Nil,
       )
 
   private[sbt] def defaultProjectSettings: Seq[Setting[_]] = Seq(

main/src/main/scala/sbt/internal/Load.scala

@@ -866,22 +866,24 @@ private[sbt] object Load {
       localBase: File,
       context: PluginManagement.Context,
       existingIDs: Seq[String]
-  ): String = {
-    def normalizeID(f: File) = Project.normalizeProjectID(f.getName) match {
+  ): String =
+    def normalizeID(f: File) = Project.normalizeProjectID(f.getName) match
       case Right(id) => id
       case Left(msg) => sys.error(autoIDError(f, msg))
-    }
     @tailrec def nthParentName(f: File, i: Int): String =
-      if (f eq null) BuildDef.defaultID(localBase)
-      else if (i <= 0) normalizeID(f)
+      if f eq null then BuildDef.defaultID(localBase)
+      else if i <= 0 then normalizeID(f)
       else nthParentName(f.getParentFile, i - 1)
     val pluginDepth = context.pluginProjectDepth
-    val postfix = "-build" * pluginDepth
+    val postfix =
+      if pluginDepth == 0 then "-root"
+      else "-build" * pluginDepth
     val idBase =
-      if (context.globalPluginProject) "global-plugins" else nthParentName(localBase, pluginDepth)
+      if context.globalPluginProject then "global-plugins"
+      else nthParentName(localBase, pluginDepth)
     val tryID = idBase + postfix
-    if (existingIDs.contains(tryID)) BuildDef.defaultID(localBase) else tryID
-  }
+    if existingIDs.contains(tryID) then BuildDef.defaultID(localBase)
+    else tryID
 
   private[this] def autoIDError(base: File, reason: String): String =
     "Could not derive root project ID from directory " + base.getAbsolutePath + ":\n" +