Hi Jacob,
What did you hope to achieve with this domain? Was it meant to be different content to your current site?
To be honest there isn't a lot of use for this domain as you would be better off putting time into your current domain. Unfortunately, people buy other keyword rich domains that aren't going to help your site in the long run. Google isn't going to associate this domain with your current one unless you plan to make it the priority and of huge value that differs to your current site. You could, of course, migrate your current website to that website but I wouldn't recommend this as it could lead to a whole lot of other issues if done incorrectly. And you could be spending this time doing other digital marketing tasks for your current site.
For your suggestions:
1. I don't really understand what you mean having an add-on to the main domain. If this is duplicate content you'd have to have it canonicalised and then it wouldn't have much benefit for your current site anyway. You'd be better off putting this content on your current domain.
2. Having a single static page wouldn't be of much worth cause wouldn't this page perform better on your current website? Adding this content to your current site would also bring your overall content quality up (assuming it is good content).
3. Redirecting this domain to your current domain wouldn't help that much, unless it's got an amazing backlink profile to bring traffic through.
Cheers