Settings › Battery › Background usage limits: make sure Chrome is not in Sleeping apps or Deep sleeping apps, and turn off Put unused apps to sleep.
Settings › Apps › Chrome › Notifications: on.
If you added this app from Samsung Internet rather than Chrome, apply the same three steps to Samsung Internet instead.
One more step
Your privacy
Turning on reminders stores only the anonymous address your
browser uses to receive them, and the date you turned them on. No name, no
phone number, no email. Tap Turn reminders off and it is deleted.