Update DevTools to next dev version (#9672)

diff --git a/packages/devtools_app/lib/devtools.dart b/packages/devtools_app/lib/devtools.dart
index 15fcb1d..9ec9fa7 100644
--- a/packages/devtools_app/lib/devtools.dart
+++ b/packages/devtools_app/lib/devtools.dart
@@ -10,4 +10,4 @@
 /// Note: a regexp in the `dt update-version' command logic matches the constant
 /// declaration `const version =`. If you change the declaration you must also
 /// modify the regex in the `dt update-version' command logic.
-const version = '2.55.0';
+const version = '2.56.0-dev.0';
diff --git a/packages/devtools_app/pubspec.yaml b/packages/devtools_app/pubspec.yaml
index 0cace3b..a5a6c65 100644
--- a/packages/devtools_app/pubspec.yaml
+++ b/packages/devtools_app/pubspec.yaml
@@ -7,7 +7,7 @@
 
 # Note: this version should only be updated by running the 'dt update-version'
 # command that updates the version here and in 'devtools.dart'.
-version: 2.55.0
+version: 2.56.0-dev.0
 
 repository: https://github.com/flutter/devtools/tree/master/packages/devtools_app
 
diff --git a/packages/devtools_app/release_notes/NEXT_RELEASE_NOTES.md b/packages/devtools_app/release_notes/NEXT_RELEASE_NOTES.md
index 79a9508..fc8c7f4 100644
--- a/packages/devtools_app/release_notes/NEXT_RELEASE_NOTES.md
+++ b/packages/devtools_app/release_notes/NEXT_RELEASE_NOTES.md
@@ -6,9 +6,9 @@
 This is a draft for future release notes that are going to land on
 [the Flutter website](https://docs.flutter.dev/tools/devtools/release-notes).
 
-# DevTools 2.55.0 release notes
+# DevTools 2.56.0 release notes
 
-The 2.55.0 release of the Dart and Flutter DevTools
+The 2.56.0 release of the Dart and Flutter DevTools
 includes the following changes among other general improvements.
 To learn more about DevTools, check out the
 [DevTools overview](/tools/devtools).
@@ -68,4 +68,4 @@
 ## Full commit history
 
 To find a complete list of changes in this release, check out the
-[DevTools git log](https://github.com/flutter/devtools/tree/v2.55.0).
+[DevTools git log](https://github.com/flutter/devtools/tree/v2.56.0).