flutter analyze cleanup (#20490)

* `flutter analyze` cleanup

* Make `--dartdocs` work in all modes.
* Make `analyze-sample-code.dart` more resilient.
* Add a test for `analyze-sample-code.dart`.
* Minor cleanup in related code and files.

* Apply review comments

* Fix tests

analysis_options.yaml

@@ -7,7 +7,9 @@
 # See the configuration guide for more
 # https://github.com/dart-lang/sdk/tree/master/pkg/analyzer#configuring-the-analyzer
 #
-# There are four similar analysis options files in the flutter repos:
+# There are other similar analysis options files in the flutter repos,
+# which should be kept in sync with this file:
+#
 #   - analysis_options.yaml (this file)
 #   - packages/flutter/lib/analysis_options_user.yaml
 #   - https://github.com/flutter/plugins/blob/master/analysis_options.yaml
@@ -15,9 +17,6 @@
 #
 # This file contains the analysis options used by Flutter tools, such as IntelliJ,
 # Android Studio, and the `flutter analyze` command.
-#
-# The flutter/plugins repo contains a copy of this file, which should be kept
-# in sync with this file.
 
 analyzer:
   language:
@@ -132,6 +131,7 @@ linter:
     - prefer_is_not_empty
     - prefer_single_quotes
     - prefer_typing_uninitialized_variables
+    # - public_member_api_docs # enabled on a case-by-case basis; see e.g. packages/analysis_options.yaml
     - recursive_getters
     - slash_for_doc_comments
     - sort_constructors_first