As long as you treat servers as cattle, you can use Hetzner's own load balancer service and then you don't have a SPOF that you manage yourself. Their LBs are advertised as redundant / fault tolerant.

My app allows for "share nothing" architecture, basically using multiple DNS A records as load balancing. Currently it has 6 servers.

Even if 5 of them would go down at the same time, the site would still work as intended (thought probably couldn't handle peak load with less than 3 or 4). If one of or two are down, nothing happens.

Also completely reinstalling a server takes around an hour.

I do not have an HA setup BUT all of my proxmox vms are snapshot backuped by proxmox backup server every night to my home NAS and to my office NAS. You can use one of many storage providers. SSHFS also works. This is the cheapest and lowest administration solution I used till today. For production usage I would recommend 3-4 similar speced 28€ machines and run a replicated proxmox cluster or ceph proxmox cluster.