Hey, yes this is possible, someone already mentioned it in this forum however I don't have any details and it might not be as easily setup as Synology Drive Client. First of all, if it should be reachable over the Internet you either need to setup a VPN or a reversed proxy with a domain. This however is true for every service which you want to reach from the Internet and not limited to the drive replacement. But once you have this setup it's easily configured for Immich and your media player if needed.
Immich is great, it's a free self hosted replacement for Google Photos.
Concerning Buddy Backup it's foreseen to come this year, but you need a second (Hexos) server (and hexos licenses if you want to run it yourself) to backup to. But even without Buddy Backup, local backups to another Hexos/Truenas server is easily done using the replication tasks.
You run do everything on the same server, this saves you the costs of having to run 2 servers and you only need to maintain 1 server. It's best to use Jellyfin or Plex (although Plex is alienating a lot of users recently which are switching to Jellyfin) on your server with an iGPU or dedicated GPU. As long as you have a decent GPU and not a lot of people streaming at the same time, performance impact is not an issue.
Stay away from Realtek NICs (they are not supported and a lot of problems reported in this forum regarding connectivity or speed were solved by replacing the realtek NIC). If you need to get a new NIC, go for an Intel 2.5 or 10 Gbit/s NIC depending on your future network upgrade plans.
Intel iGPUs are great for media streaming/transcoding and you don't need a dedicated GPU just for this. Immich does leverage a dedicated GPU for Machine Learning stuff but doesn't warrant a dedicated GPU just for this purpose.
You need at least 2 data drives and 1 small boot drive. The boot drive can't be used for anything else then the OS so don't use a 1TB drive for this, a 16GB SSD is enough. With 2 data drives, Hexos is creating a mirrored pool which is not expandable in size, therefore you need to create a pool with at least 3 data drives to be able to expand in the future. Stay away from SMR drives (Desktop drives or WD RED (non plus, non pro)) make sure to only go for CMR drives.
If you want to get new HW or reuse your existing server, you can post the components in here and you will get help to match the parts as best as possible and avoid certain pitfalls.