Update dartdoc to 0.44.0. (#83352)

dev/bots/docs.sh

@@ -20,7 +20,7 @@ function generate_docs() {
     # Install and activate dartdoc.
     # NOTE: When updating to a new dartdoc version, please also update
     # `dartdoc_options.yaml` to include newly introduced error and warning types.
-    "$PUB" global activate dartdoc 0.43.0
+    "$PUB" global activate dartdoc 0.44.0
 
     # This script generates a unified doc set, and creates
     # a custom index.html, placing everything into dev/docs/doc.