[M106] Add `WebStorage` to paths to be moved to Lacros.

Adding `WebStorage` to paths to be moved to Lacros, which was added
after the last audit.

(cherry picked from commit 1e19fa9165dbd8f98f9cb135bc318810a7e6dc3f)

Bug: 1362103
Change-Id: Ia7037f7776504669c96ddf1fda66a667c37f1489
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3925140
Reviewed-by: Erik Chen <[email protected]>
Reviewed-by: Ayu Ishii <[email protected]>
Commit-Queue: Yuta Hijikata <[email protected]>
Cr-Original-Commit-Position: refs/heads/main@{#1053380}
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3944228
Cr-Commit-Position: refs/branch-heads/5249@{#804}
Cr-Branched-From: 4f7bea5de862aaa52e6bde5920755a9ef9db120b-refs/heads/main@{#1036826}
diff --git a/chrome/browser/ash/crosapi/browser_data_migrator_util.h b/chrome/browser/ash/crosapi/browser_data_migrator_util.h
index 7390865..9e2ee461 100644
--- a/chrome/browser/ash/crosapi/browser_data_migrator_util.h
+++ b/chrome/browser/ash/crosapi/browser_data_migrator_util.h
@@ -180,7 +180,8 @@
     "Top Sites",
     "Visited Links",
     "Web Applications",
-    "Web Data"};
+    "Web Data",
+    "WebStorage"};
 
 // The base names of files/dirs that are required by both ash and lacros and
 // thus should be copied to lacros while keeping the original files/dirs in ash