Add a real-er web restart, doctor, workflow (#33786)

dev/devicelab/manifest.yaml

diff --git a/dev/devicelab/manifest.yaml b/dev/devicelab/manifest.yaml
index 0c976c9..581bbeb 100644
--- a/dev/devicelab/manifest.yaml
+++ b/dev/devicelab/manifest.yaml
@@ -125,6 +125,13 @@
     stage: devicelab_win
     required_agent_capabilities: ["windows/android"]
 
+  windows_chrome_dev_mode:
+    description: >
+      Run flutter web on the devicelab and hot restart.
+    stage: devicelab_win
+    required_agent_capabilities: ["windows/android"]
+    flaky: true
+
   # Android on-device tests
 
   complex_layout_scroll_perf__timeline_summary:
@@ -324,6 +331,13 @@
     stage: devicelab
     required_agent_capabilities: ["linux/android"]
 
+  linux_chrome_dev_mode:
+    description: >
+      Run flutter web on the devicelab and hot restart.
+    stage: devicelab
+    required_agent_capabilities: ["linux/android"]
+    flaky: true
+
   # iOS on-device tests
 
   flavors_test_ios:
@@ -421,6 +435,13 @@
     stage: devicelab_ios
     required_agent_capabilities: ["mac/ios"]
 
+  macos_chrome_dev_mode:
+    description: >
+      Run flutter web on the devicelab and hot restart.
+    stage: devicelab_ios
+    required_agent_capabilities: ["mac/ios"]
+    flaky: true
+
   # Tests running on Windows host
 
   flavors_test_win: