fix(firehose): bump dependency_validator to support analyzer 14

Bump dependency_validator pinned commit hash to 52f142e104371eab25d56cafef127ee53b715d22 to support analyzer 14 (and doc directives such as {@example}).
diff --git a/pkgs/firehose/CHANGELOG.md b/pkgs/firehose/CHANGELOG.md
index 207567d..4705c46 100644
--- a/pkgs/firehose/CHANGELOG.md
+++ b/pkgs/firehose/CHANGELOG.md
@@ -3,8 +3,8 @@
 - Document Zizmor compatibility and ignore syntax for `post_summaries.yaml`.
 - Update `post_summaries.yaml` to resolve PR numbers for fork workflow runs via
   commit SHA, and verify comment authorship when checking `commentId`.
-- Update `dependency_validator` pinned commit hash to 5.0.6 (`7582a808960d2170800bfbd7a83526619ce300ce`),
-  enabling support for newer Dart syntax (up to analyzer 13).
+- Update `dependency_validator` pinned commit hash to `52f142e104371eab25d56cafef127ee53b715d22`,
+  enabling support for newer Dart syntax and analyzer 14 (e.g. `{@example}` doc directives).
 - Update existing publishing PR comments with accurate status when packages are
   no longer ready to publish (e.g. when updated to `-wip`).
 - Add `delete` command to `firehose:comment` executable.
diff --git a/pkgs/firehose/lib/src/health/health.dart b/pkgs/firehose/lib/src/health/health.dart
index fc44600..1faac29 100644
--- a/pkgs/firehose/lib/src/health/health.dart
+++ b/pkgs/firehose/lib/src/health/health.dart
@@ -25,7 +25,7 @@
 
 /// To allow easier searching for the package name
 // ignore: constant_identifier_names
-const dependency_validatorHash = '7582a808960d2170800bfbd7a83526619ce300ce';
+const dependency_validatorHash = '52f142e104371eab25d56cafef127ee53b715d22';
 
 enum Check {
   license('License Headers', 'license'),