How would I go about creating a github action to deploy a dotnet app to an existing droplet - without docker?
If that's not possible, can I SSH into the droplet using a pwd and running a command inside of it?
DigitalOcean API and CLI (doctl)
What would be the best way to run the setup above?
Can they run without a docker on a linux machine?
Yes you should be able to run that on an Ubuntu 16 droplet.
To install MSSQL(mssql-server) follow these steps here:
Import the public repository GPG keys: