madebyraygun I'd just like to 2nd this post - you can "deploy from Github" with Enhance already, just by running a Git command to pull down the repo, that functionality already exists. But by doing that, you're completely missing the entire BUILD part of the process.
Generally speaking, you shouldn't have the entire ready-to-go website in your repository - you don't version control that which you can retrieve as a dependency, so the idea of deploying straight from Github isn't especially useful anyway. In almost every scenario, you should be executing some build / test steps after fetching the repo, so it really comes down to WHERE you would like to execute those steps.
You can do that, right now, on your host. Write a bash script to pull down the repo, run Composer, copy stuff around, set permissions, so on and so on. You can even execute a full testing suite on the host if you really want to! This is of course, not a great idea for a production environment - you're chewing up a LOT of resources, running things that really have no business being run on your live servers.
So this is why using Github Actions is THE solution to this problem. It's entirely contained within Github - you don't need third party products and licensing. It executes the build / tests completely offsite, meaning all that resource usage goes nowhere near your live servers, and then, once absolutely everything is done, it deploys the final built product to your production environment.
If anyone is genuinely interested, I've been doing this kind of agency-level DevOps for well over a decade now, so I'm happy to give some free advice / provide consultancy services. Just hit me up, we can have a chat!