Update the root project name check in publish.gradle

The name was changed in androidx/media@2558138
and this check wasn't updated, meaning publishing no longer worked
(it didn't publish anything, just printed lots of warnings like
`Skipping task ':test-utils-robolectric:publish' as it has no
actions.`). This change means the check is now using the same
source-of-truth as the root project name, so it shouldn't go out of
sync again.

#minor-release

PiperOrigin-RevId: 531457952

core_settings.gradle

@@ -21,6 +21,8 @@ if (gradle.ext.has('androidxMediaModulePrefix')) {
     modulePrefix += gradle.ext.androidxMediaModulePrefix
 }
 
+rootProject.name = gradle.ext.androidxMediaProjectName
+
 include modulePrefix + 'lib-common'
 project(modulePrefix + 'lib-common').projectDir = new File(rootDir, 'libraries/common')
 

publish.gradle

@@ -16,7 +16,7 @@ apply plugin: 'maven-publish'
 apply from: "$gradle.ext.androidxMediaSettingsDir/missing_aar_type_workaround.gradle"
 
 afterEvaluate {
-    if (rootProject.name == "media3") {
+    if (rootProject.name == gradle.ext.androidxMediaProjectName) {
         publishing {
             repositories {
                 maven {

settings.gradle

@@ -18,7 +18,7 @@ if (gradle.ext.has('androidxMediaModulePrefix')) {
     modulePrefix += gradle.ext.androidxMediaModulePrefix
 }
 
-rootProject.name = 'androidx.media3'
+gradle.ext.androidxMediaProjectName = 'androidx.media3'
 
 include modulePrefix + 'demo'
 project(modulePrefix + 'demo').projectDir = new File(rootDir, 'demos/main')