I don’t think that transitioning tool exists yet. You will have to do it manually. It is not that hard but bit laborious. I have been able to reproduce Bluefin-DX on a fresh Silverblue 40 (no rebasing), by following the steps in the bluefin repository here, in my attempt to debug the vscode integration with distroboxes.
I am not familiar with Aurora or Bazzite regarding Docker. If Docker is not installed, you will have to install it first by layering it. First step before installing it is to add the docker-ce repository to /etc/yum.repos.d, which you can do by saving a file from the repo above. And then you will be ready to install Docker.
The installation of podman, Distrobox is straight forward by layering them. I suggest you install Docker and DevContainers extension first and test all of their capabilities fully working before adding more packages, meaning Podman or Distrobox. There are two fixes necessary to make Docker work in a Silverblue derivative: (i) enabling and starting the docker service; (ii) manually adding the user to the docker group. Test if, at least, the minimal docker run hello-world runs without errors, before venturing in vscode.
When the moment of installing vscode comes, you will have the choice of flatpak-vscode vs layered-vscode. The former requires a bit of tinkering with scripts for docker, podman and distroboxes, while the latter saves you the extra tinkering on the docker side. Still, you will need to add couple of scripts to layered-vscode to enable it to see podman or distrobox containers; a one line script, really. If your objective includes also logging in container terminals, with flatpak-vscode then you will need to add few lines to vscode on the the terminal integration profiles to spawn a terminal in bash or zsh.
To make Docker and DevContainers work with vscode (layered or flatpak) you really don’t need podman, distrobox, or BoxBuddy.
You can read more about the tests I am running to make vscode (flatpak and layered) integration work with Docker, Podman and Distrobox here.