Try a go at this https://group-mail.com/managing-email-lists/how-to-create-an-email-newsletter-opt-in-subscription-form-for-your-website/

This is something you need to do through your Domain provider. If you pay with it through a host that has cPanel then you can simply login to cPanel and start adding emails. I would recommend getting this setup through an actual host though rather than a domain/host site such as name cheap or godaddy. These two sites have extremely pricy email hosting services which can cost up to 10.00$ per month, per email. Whereas many hosts have this feature integrated for free or for a small additional price.

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Why use something ingame? Unless you want to link it with specific events, which I'm very sure would be a premium function at best and a custom paid plugin more likely, then there's no apparent point. Generally, an email created for the server suffices.

The closest I'm aware of for this is XMPP, which can be explored by the accessible EssentialsXMPP plugin. It would take a good deal of config work, and how well it actually works depends on what you're trying to do.

Then the obligatory mention of the entirely ingame /mail function, which I'm pretty sure you already know of, but I'll mention anyways for the Essentials plugin as well. Any Gmail link for that would probably be a pricey custom dev.