Ensure rootProject.name is only set from settings.gradle

I moved this assignment in 0888dfbd05
in order to provide a single source-of-truth for `publish.gradle`,
but as pointed out in Issue: androidx/media#416 this breaks apps that are depending
on our project locally using the instructions we publish. Instead we can
remove the `rootProject.name` check from `publish.gradle`, and check an
explicit boolean value instead to indicate if the root project is 'ours'
(with this boolean only set from `settings.gradle`, so it doesn't get
picked up by apps depending on us locally).

#minor-release

PiperOrigin-RevId: 534459085
(cherry picked from commit 9a79571284)

core_settings.gradle

@@ -21,8 +21,6 @@ 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 == gradle.ext.androidxMediaProjectName) {
+    if (gradle.ext.has('rootProjectIsAndroidXMedia3') && gradle.ext.rootProjectIsAndroidXMedia3) {
         publishing {
             repositories {
                 maven {

settings.gradle

@@ -18,7 +18,8 @@ if (gradle.ext.has('androidxMediaModulePrefix')) {
     modulePrefix += gradle.ext.androidxMediaModulePrefix
 }
 
-gradle.ext.androidxMediaProjectName = 'androidx.media3'
+rootProject.name = 'androidx.media3'
+gradle.ext.rootProjectIsAndroidXMedia3 = true
 
 include modulePrefix + 'demo'
 project(modulePrefix + 'demo').projectDir = new File(rootDir, 'demos/main')