If you don't want to go down the NFS share route then Capistrano is a useful tool if you're willing to write a little bit of ruby. It comes with some built in goodies like rollbacks. It's an oldie (pre-dockerize everything), but still useful.

https://github.com/capistrano/capistrano

You can start by deploying from your machine to simultaneously get it deploying across all your servers, then I'd consider having a CI/CD pipeline take over and run Capistrano for you.