You aren't helpless in the face of email newsletter overwhelm. Take charge of what makes it into your inbox and control what you spend your energy and attention on at work.
Gmail offers some wonderful and simple keyboard shortcuts to help you manage your inbox at light speed.
You can have labels automatically applied to incoming Gmail emails based on a number of criteria - sender, subject line, even a specific phrase appearing in the email body. It's an easy trick to keep your inbox well-organized and manageable.
Email overwhelm is one of the most common technology complaints that I hear from clients. The good news is that if your email is run through Gsuite or Gmail's web interface there's a plethora of simple tools you can take advantage of to tame your email influx.