SystemNotificationManagerTest: Simplify test code

BUG=b:283709278
TEST=unit_tests --gtest_filter=SystemNotificationManagerTest.*

Change-Id: I4bc300eab295adb6cc3bf2e03adfe0fe9bc6c1c9
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4570181
Commit-Queue: François Degros <fdegros@chromium.org>
Commit-Queue: Ben Reich <benreich@chromium.org>
Auto-Submit: François Degros <fdegros@chromium.org>
Reviewed-by: Ben Reich <benreich@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1150390}