Use partition intead of "root" to assemble filesystem artifacts

The artifacts for filesystem packaging are currently assembled in
```
$intermediates/$module/android_common/root/$base_dir
```

This CL changes this to
```
$intermediates/$module/android_common/$partition/$base_dir
e.g.
$intermediates/$module/android_common/system/system (system)
$intermediates/$module/android_common/system_ext (system_ext)
```

The motivatiton for this change is to fix diffs in
BuildManifestSystemExt.apk. The build_manifest.pb of this apk is
generated from the base of $PRODUCT_OUT. This means that the paths of
the artifacts contains the partition prefix. diff https://diff.googleplex.com/#key=9xuSx7nvP251

An alternative would be to use partition as the `Base_dir`, but this
would create an additional top-level directory in the soong img files
(make img files do not have a top-level partition directory for non
system images)

Test: 383144733
Bug: Built and mounted make and soong system_ext.img for AOSP CP. NOTICE
is the last diff

Change-Id: Iee53113a7e00dcda9d987f2aabf9605740bbe7fe
diff --git a/filesystem/filesystem.go b/filesystem/filesystem.go
index b9cb076..81afd02 100644
--- a/filesystem/filesystem.go
+++ b/filesystem/filesystem.go
@@ -457,7 +457,7 @@
 }
 
 func (f *filesystem) appendToEntry(ctx android.ModuleContext, installedFile android.Path) {
-	partitionBaseDir := android.PathForModuleOut(ctx, "root", proptools.String(f.properties.Base_dir)).String() + "/"
+	partitionBaseDir := android.PathForModuleOut(ctx, f.rootDirString(), proptools.String(f.properties.Base_dir)).String() + "/"
 
 	relPath, inTargetPartition := strings.CutPrefix(installedFile.String(), partitionBaseDir)
 	if inTargetPartition {
@@ -547,8 +547,12 @@
 	builder.Command().Textf("cp -prf %s/* %s", rebasedDir, installPath)
 }
 
+func (f *filesystem) rootDirString() string {
+	return f.partitionName()
+}
+
 func (f *filesystem) buildImageUsingBuildImage(ctx android.ModuleContext) android.Path {
-	rootDir := android.PathForModuleOut(ctx, "root").OutputPath
+	rootDir := android.PathForModuleOut(ctx, f.rootDirString()).OutputPath
 	rebasedDir := rootDir
 	if f.properties.Base_dir != nil {
 		rebasedDir = rootDir.Join(ctx, *f.properties.Base_dir)
@@ -775,7 +779,7 @@
 		ctx.PropertyErrorf("include_make_built_files", "include_make_built_files is not supported for compressed cpio image.")
 	}
 
-	rootDir := android.PathForModuleOut(ctx, "root").OutputPath
+	rootDir := android.PathForModuleOut(ctx, f.rootDirString()).OutputPath
 	rebasedDir := rootDir
 	if f.properties.Base_dir != nil {
 		rebasedDir = rootDir.Join(ctx, *f.properties.Base_dir)