[Build] Migrate most of the build logic from Project.buildDir usage

It's going to be deprecated in Gradle 8.3

There's currently no way to pass a `org.gradle.api.provider.Provider` to the JavaExec.systemProperty or Test.systemProperty. There's a workaround using `org.gradle.process.CommandLineArgumentProvider`, but I intentionally don't rework these calls as Gradle is going to allow passing providers to configure system properties: https://github.com/gradle/gradle/issues/12247#issuecomment-1568427242
^KTI-1473 In Progress

build.gradle.kts

@@ -692,14 +692,17 @@ tasks.register("createIdeaHomeForTests") {
     val intellijSdkVersion = rootProject.extra["versions.intellijSdk"]
     outputs.file(ideaBuildNumberFileForTests)
     doFirst {
-        ideaBuildNumberFileForTests.parentFile.mkdirs()
-        ideaBuildNumberFileForTests.writeText("IC-$intellijSdkVersion")
+        with(ideaBuildNumberFileForTests.get().asFile) {
+            parentFile.mkdirs()
+            writeText("IC-$intellijSdkVersion")
+        }
     }
 }
 
 tasks {
     named<Delete>("clean") {
-        delete += setOf("$buildDir/repo", distDir)
+        delete(distDir)
+        delete(layout.buildDirectory.dir("repo"))
     }
 
     register<Delete>("cleanupArtifacts") {
@@ -1046,7 +1049,7 @@ val zipCompilerWithSignature by secureZipTask(zipCompiler)
 configure<IdeaModel> {
     module {
         excludeDirs = files(
-            project.buildDir,
+            project.layout.buildDirectory,
             commonLocalDataDir,
             ".gradle",
             "dependencies",