👋 To my knowledge, we don't have documented best practices specifically around the UI, the closest we have is
this overview of running meltano in production.
The best practices for deploying the UI might vary depending on your current stack and use cases for the UI. In general though, as long as running instances of the UI and API server are reading from and writing to the same backend db and are preferably set to readonly so your meltano.yml is identical across instances, you can safely scale meltano horizontally and then load balance across instances.
Hope that helps!