It shouldn't really scale above a certain point, it's just that if you import a lot of pictures all at once (in my case with immich-go, as mentioned from a Google photos takeout), all the ML-Tasks (facial recognition, search tagging) together with the normal tasks (thumbnail extraction, video transcoding) can suddenly increase the ram usage from in my case normally 1-2gb to around 6, which even on an 8gb raspi could get a little tight. But for example even just 16gb in the HP should be enough, assuming you don't have a bunch of other stuff clogging up your RAM. As for the CPU, I'm not too sure tbh, I'm using a Ryzen 5 5600G, which can handle everything that's running on my server with ease. I think the only significant downside you'd have here going with 4th gen is power efficiency. I still have an i7 6850K (OCd to 4.3GHz) in my main PC, and that thing uses a couple hundred watts when fully loaded, compared to my Ryzens 65W or so. If you're just going for an i5 or i3 with the fourth gen that's probably not gonna matter too much, but the performance probably also won't be amazing at the same time.
Technikus5
I'd also highly recommend the proper PC, Immich can get pretty RAM-hungry if you use the ML functions, for me that has actually caused crashes before. Granted, that was while importing roughly 20k Assets (200GB) from a Google photos takeout, but it's still probably better to be prepared.
To be fair though, those warnings are not really representative of the current user experience. I've had Immich running for about 6 months by now, and apart from the very frequent updates the only annoyance was when they recently changed their database scheme, and I had to manually add two extensions to my Postgres. Everything else has been rock solid, and has been improving at a massive pace
I'd recommend I'm mich instead of Photoprism, at least for this usecase. I have both running, but I use Photoprism primarily to organize and share pictures taken with my SLR, while Immich handles Automatic Backups and sorting of all the pictures I take with my phone. Additionally Immich has way better (and still offline) facial detection, it's almost scary how good it is sometimes
I've set up several instances in circumstances like yours. The easiest way is to create a duckdns domain for yourself, and install their updater on one of your systems, to keep your external IP up to date with their DNS-Servers. Then you can use a DNS-Provider of your choice (I use Cloudflare) to create a "CNAME" DNS Record, that basically just tells a browser to redirect from your domain to the IP Address of the duckdns domain. That way you can have an automatically updating public IP behind your domain name. Then you "just" have to set up a reverse proxy (I use Nginx Proxy Manager, but there are newer and easier alternatives), and create the correct port forwarding rules in your router/firewall, and you should be good to go