I've needed to do this several times to combat "ghost" notifications. These occur when a discussion is created and then deleted (e.g. for spam) before the notofication is read. You may see something like "1-0 of 4" at the bottom of the notifications page.
You can use the GitHub API client to show these notifications:
gh api notifications
To mark all notifications as read, send the API request below with curl. (Update the last_read date as needed.)