I would suggest looking at Syncthing. It’s not perfect by any stretch, but it works peer to peer, without any kind of central host, ip or domain name requirements. You simply install it on the client machines, and they work out how to talk to each other over any available networks.

Beware changing the casing on your files or directories though, Syncthing was made entirely case sensitive, which does not play nice with Windows.

One very nice feature is that it does have an android client (https://f-droid.org/en/packages/com.github.catfriend1.syncthingandroid/), and it supports full background syncing to your local storage on the phone. Great for syncing your photos, but also music. You add some mp3’s on your desktop computer, and by the time you’ve put on your jacket they’re on your phone ready to listen to without any ‘service’ getting in your way.

A more advanced tip; Get a VPS somewhere in the cloud with cheap storage, and have Syncthing on it listening on port 443. That will allow syncing in more restrictive corporate settings, which often don’t allow connections to port 22000. And it gives you a ‘cloud backup’ of your important files in one go.

Proxmox is Debian. :-)
I do always suggest installing Debian first, and then installing Proxmox on top. This allows you to properly set up your disks, and networking as needed, as the Proxmox installer is a bit limited: https://pve.proxmox.com/wiki/Install_Proxmox_VE_on_Debian_12_Bookworm
Once you have it up and running, have a look at the CT Templates. There’s a whole set of pre-configured templates from TurnkeyLinux (again, debian+) that make it trivial to set up all kinds of services in lightweight LXC Containers.
For Home Assistant a VM is your best bet, as it makes setting up connectivity way easier than messing with docker networking. It also allows easy USB passthrough, for things like ZWave/Zigbee/Bluetooth adapters.