Yeah you can to that. I did this like you when I started with my homelab. I used podman very fast after playing with docker. You can just replace docker with podman ex:

podman pull x
podman run x
podman compose up

Podman has better rootless support and is a bit more secure because of that.

Just a few tips (optional but I recommend you)

• Do not run container as root: If you run a container as root and the container gets hijacked someone could start/stop container on your behalf and since it would be possible to mount the root fs to the container they would be able to hijack the os. Do not mount the docker socked into the container unless you really trust the process and know the risks.
• UID/GID should not match with the hosts: If you share the same UID (1000) from your user and then the container has the same UID inside it, then they have technically the same permission set as your home directory or worse root directory (if UID is 0) and could do harm if they are exploited and can break free of the container
• Remember to stay up to date: Go on Vaultwarden GitHub and subscribe to notifications about "Security" and "Releases". Since I would use podman over docker you could have a look into podman auto updates feature.
• Limit container resources: Just do it. No downsides. Limit CPU and RAM usage of the container via the compose.yml file. If someone hacks the container they can't mine bitcoin on it so easily and it chills your server abit. Here is how you can do that.

Kubernetes is a bit overkill and bloated for your usecase. Kubernetes would be interesting if you host a service with world wide access and millions of parralel users because of the nice scaling functionality of kubernetes.

What ever you do you did the right choice to learn something new, and I wish you fun and joy doing this! When I started vs today I learned many new things and practices which helped me earn money and have fun!