I'm running podman and podman-compose with no problem. And I'm happy. At first I was confused by the uid and gid mapping the containers have, but you'll get used to it.
This are some notes I took, please don't take all of it for the right choice.
Then point that record to 127.0.0.0. This will not resolve for anyone. But you'll have an internal dns enty (useig pihole/adguard/unbound) that redirects to your reverse proxy.
You could also point to your revers proxy internal address instead of 127.0.0.0.
I switched a year ago to podman and had some trouble to get everything running. But it is possible. I'm not running anything rootful and everything works.
Read the docs, use podman-compose (this sadly has no good docs, but works quit well when you got it) and get ready to play around with permissions and file ownership.
As far as I know, you'll have a last syched copy in your cache. Test it with no internet con! Try to export your data without internet.
I'm using vaultwarden for like 4 year now, but on my personal server at home. Btw a raspberry pi is enough to run vaultwarden.
You could take a look at reverse proxys and dyndns services (like duckdns -> free).
I started like this. Now I have my own domain, but that is not mandatory!
how are you trying to run podman?
If you just want a similar setup as with docker I'll recommend this:
https://github.com/containers/podman/blob/main/docs/tutorials/rootless_tutorial.md
Lingering (running services without login / after logout)
https://github.com/containers/podman/issues/12001
https://unix.stackexchange.com/questions/462845/how-to-apply-lingering-immedeately#462867
https://github.com/containers/podman/blob/main/vendor/github.com/containers/storage/storage.conf
Check out the storage.conf to use the fuse-overlay driver.
I like podman-compose and i have a start up script that restarts all my containers at reboot, as my user.
Also use the full link to your images, like docker.io/image oder where ever you get your images from.
have fun :)