There's no formal recommendation for how to integrate with FusionAuth, other than the APIs.
The way I'd build pages and logic that I wanted side by side (like a login page which required two factor auth for a given application 🙂 ) with FusionAuth would be to proxy fusionauth with something like an ALB or nginx. Then have one path for fusionauth login pages and another path for your custom application. You could pull the retrieve the theme CSS and reuse it.
The only plugins that FusionAuth supports right now are for password importing.
The java client library of course is available for integration, but if you are building a side by side webapp, I'd use whatever client library makes sense for your environment.
But perhaps I'm not sure what you're trying to accomplish with this integration. Would you like one deployable artifact or something similar? Can you explain more?