For no 1, that shouldn’t be dind, the container would be controlling the host docker, wouldn’t it?
If so, keep in mind that this is the same as giving root SSH access to the host machine.
As far as security goes, anything that allows GitHub to cause your server to download (pull) and use a set of arbitrary of Docker images with arbitrary configuration is remote code execution. It doesn’t really matter what you to secure access to the machine, if someone compromises your GitHub account.
I would probably set up SSH with a key dedicated to GitHub, specifically for deploying. If SSH is configured to only allow keys for access, it’s not much of a security risk to open it up to the internet. I would then configure that key to only be able to run a single command, which I would make a very simple bash script which runs git fetch, and then git verify-commit origin/main (or whatever branch you deploy), befor checking out the latest commit on that branch.
You can sign commits fairly easily using SSH keys now, which combined with the above allows you to store your data on GitHub without having to trust them to have RCE on your host.