Move plugin injection to just after pub get (#14743)

dev/devicelab/manifest.yaml

diff --git a/dev/devicelab/manifest.yaml b/dev/devicelab/manifest.yaml
index 63b3d1f..27a0bfc 100644
--- a/dev/devicelab/manifest.yaml
+++ b/dev/devicelab/manifest.yaml
@@ -237,6 +237,13 @@
     stage: devicelab
     required_agent_capabilities: ["linux/android"]
 
+  plugin_test:
+    description: >
+      Checks that the project template works and supports plugins.
+    stage: devicelab
+    required_agent_capabilities: ["linux/android"]
+    flaky: true
+
   flutter_gallery_instrumentation_test:
     description: >
       Same as flutter_gallery__transition_perf but uses Android instrumentation
@@ -253,6 +260,13 @@
     stage: devicelab_ios
     required_agent_capabilities: ["mac/ios"]
 
+  plugin_test_ios:
+    description: >
+      Checks that the project template works and supports plugins on iOS.
+    stage: devicelab_ios
+    required_agent_capabilities: ["mac/ios"]
+    flaky: true
+
   external_ui_integration_test_ios:
     description: >
       Checks that external UIs work on iOS.
@@ -347,6 +361,13 @@
     stage: devicelab_win
     required_agent_capabilities: ["windows/android"]
 
+  plugin_test_win:
+    description: >
+      Checks that the project template works and supports plugins on Windows.
+    stage: devicelab_win
+    required_agent_capabilities: ["windows/android"]
+    flaky: true
+
   hot_mode_dev_cycle_win__benchmark:
     description: >
       Measures the performance of Dart VM hot patching feature on Windows.