[flutter_plugin_tools] Simplify filesystem usage (#4014)

- Replaces most explicit use of `fileSystem` with path construction using the `child*` utility methods
- Removes explicit passing of a filesystem to the commands; we're already passing a `Directory` for the
  root where the tool operates, and we should never be using a different filesystem than that directory's
  filesystem, so passing it was both redundant, and a potential source of test bugs.

script/tool/lib/src/pubspec_check_command.dart

@@ -19,12 +19,10 @@ import 'common.dart';
 class PubspecCheckCommand extends PluginCommand {
   /// Creates an instance of the version check command.
   PubspecCheckCommand(
-    Directory packagesDir,
-    FileSystem fileSystem, {
+    Directory packagesDir, {
     ProcessRunner processRunner = const ProcessRunner(),
     GitDir? gitDir,
-  }) : super(packagesDir, fileSystem,
-            processRunner: processRunner, gitDir: gitDir);
+  }) : super(packagesDir, processRunner: processRunner, gitDir: gitDir);
 
   // Section order for plugins. Because the 'flutter' section is critical
   // information for plugins, and usually small, it goes near the top unlike in