[analyzer] Pass ProcessStartMode to Process.start in ProcessRunner.start

Change-Id: I24c0725f024fcd24b189eea64e8816c4ab341520
Reviewed-on: https://dart-review.googlesource.com/c/sdk/+/445061
Reviewed-by: Samuel Rawlins <srawlins@google.com>
Commit-Queue: Samuel Rawlins <srawlins@google.com>

pkg/analysis_server/lib/src/utilities/process.dart

@@ -23,6 +23,7 @@ class ProcessRunner {
       environment: environment,
       includeParentEnvironment: includeParentEnvironment,
       runInShell: runInShell,
+      mode: mode,
     );
   }
 }