personalization: move browsertests to mojom modules

Refactor personalization_app_browsertest.js to use mojom
modules and mocha.

Bug: b:264461204
Test: browser_tests --gtest_filter=*PersonalizationApp*
Change-Id: I765c8682e81d950e5530139f747e6a669a642139
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4343963
Reviewed-by: Erica Lee <ericamlee@google.com>
Commit-Queue: Jeffrey Young <cowmoo@google.com>
Cr-Commit-Position: refs/heads/main@{#1119653}

chrome/test/data/webui/BUILD.gn

@@ -233,7 +233,6 @@ if (include_js_tests) {
         "chromeos/firmware_update/firmware_update_browsertest.js",
         "chromeos/office_fallback/office_fallback_browsertest.js",
         "chromeos/os_feedback_ui/os_feedback_browsertest.js",
-        "chromeos/personalization_app/personalization_app_browsertest.js",
         "chromeos/scanning/scanning_app_browsertest.js",
         "chromeos/shimless_rma/shimless_rma_browsertest.js",
         "nearby_share/nearby_browsertest.js",
@@ -265,6 +264,7 @@ if (include_js_tests) {
         "chromeos/diagnostics/diagnostics_browsertest.js",
         "chromeos/manage_mirrorsync/manage_mirrorsync_browsertest.js",
         "chromeos/parent_access/parent_access_browsertest.js",
+        "chromeos/personalization_app/personalization_app_browsertest.js",
         "chromeos/personalization_app/personalization_app_component_browsertest.js",
         "chromeos/personalization_app/personalization_app_controller_browsertest.js",
         "chromeos/print_management/print_management_browsertest.js",