There's just a cookie prompt and then a newsletter sign-up a little later? I don't think there's any constant bombardment, if there is for you I'm interested to know more.
1. cookies 2. email newsletter 3. cookies again
The constant bombardment was more in reference to the state of the web generally. Popups and overlays that aren't a result of an interaction I've chosen to make are exhausting for me (and people with ADHD generally, and many others). I don't go back to sites that have them, but would be happy to read (and often pay for) the content if that wasn't the context.