Cleanup dependencies in Room

- Bump room-paging to latest stable version of paging
- Remove unnecesary redundant declarations now that b/155802460 is fixed
- Change project dependency in androidTest to the same version on main
  classpath. b/135511018 for some context, the TL;DR is that
  dependencies on the main and test classpath cannot diverge and that
  AGP somehow fails to detect it in this case.

Test: ./gradlew :room:integration-tests:room-testapp-kotlin:cC
Change-Id: I1327ca7397ca35beeb5f5a97b1d5a1048e105ee8
diff --git a/room/integration-tests/kotlintestapp/build.gradle b/room/integration-tests/kotlintestapp/build.gradle
index 128ef22..00e68bc 100644
--- a/room/integration-tests/kotlintestapp/build.gradle
+++ b/room/integration-tests/kotlintestapp/build.gradle
@@ -86,7 +86,6 @@
             project(path: ":room:room-compiler", configuration: "shadowAndImplementation")
     )
     androidTestImplementation(projectOrArtifact(":lifecycle:lifecycle-livedata-ktx"))
-    androidTestImplementation(projectOrArtifact(":arch:core:core-runtime")) // Added for b/155802460
     androidTestImplementation(libs.testExtJunit)
     androidTestImplementation(libs.testCore)
     androidTestImplementation(libs.testRunner) {
@@ -100,14 +99,13 @@
     androidTestImplementation(libs.truth)
     androidTestImplementation(libs.kotlinTest)
     androidTestImplementation(project(":room:room-guava"))
-    androidTestImplementation(project(":room:room-paging")) // Added for b/155802460
     androidTestImplementation(project(":room:room-testing"))
     androidTestImplementation(project(":room:room-rxjava2"))
     androidTestImplementation(project(":room:room-rxjava3"))
     androidTestImplementation(project(":room:room-ktx"))
     androidTestImplementation(project(":internal-testutils-common"))
     androidTestImplementation("androidx.arch.core:core-testing:2.0.1")
-    androidTestImplementation(projectOrArtifact(":paging:paging-runtime"))
+    androidTestImplementation("androidx.paging:paging-runtime:3.1.1")
     androidTestImplementation(libs.guavaAndroid)
     androidTestImplementation(libs.rxjava2)
     testImplementation(libs.mockitoCore)
diff --git a/room/room-paging/build.gradle b/room/room-paging/build.gradle
index 84367bf..e1a2e69 100644
--- a/room/room-paging/build.gradle
+++ b/room/room-paging/build.gradle
@@ -47,7 +47,7 @@
 
     api(project(":room:room-runtime"))
     implementation(project(":room:room-ktx"))
-    api("androidx.paging:paging-common:3.1.0")
+    api("androidx.paging:paging-common:3.1.1")
 
     androidTestImplementation(libs.kotlinCoroutinesTest)
     androidTestImplementation(libs.multidex)