With Proxmox it's quite easy, you can copy the VM/LXC Backups to the new host (via SCP, NFS or whatever) and restore there. Recently did exactly that.

In Home Assistant, navigate to Settings > System > Backups. Configure the backup settings and create a manual backup.

On your new Proxmox server, you can download the qcow2 file from Home Assistant's website and run it as a virtual machine.

On first boot, you can import your previous configuration from a backup.

When you upgrade your desktop PC, plan for it to be the home server after that.

I got a rackmount case to transplant my old desktop montherboard into every 5 years. I also got a 4-port NIC so it can also be a router. My server is a 4th gen Core i5 and it's still plenty of power for a home server.

If you're a laptop guy, I'm not sure what you'd do. Maybe ask friends for their old desktops. The Win10 discontinuation next month would be a great opportunity to snap up some business PCs destined for landfill.

For Home Assistant, I think you either need Docker or a dedicated box. I kinda hate how there isn't a .deb package for it like literally every other service on my server.

If you can, I'd skip the laptop and go for a used workstation SFF now. $250 or so would buy you plenty of server.

All my backups are tested, so upgrades (or recovering from a failure) are usually straightforward. The only thing I don't back up is my collection of Linux ISOs, but that I can easily reacquire.