It seems pretty straightforward that tracking deliverability, opens, and click-through of your newsletter is essential in providing a newsletter service.
These metrics are fairly essential if you want to be sure your users are actually receiving your content, and what content they are relating to in order to improve your content.
Since providing relevant content which actually makes it into your users’ Inboxes is the whole point of a newsletter, it seems like ensuring that is actually happening is a core part of the service.
But I am not a lawyer, and I am certainly no expert on GDPR.