It'll definitely be more expensive than a console, since they sell the consoles at a loss expecting to make it back on the games. (But not that much more.)
... Especially in this fucking economy when it seems they're deliberately trying to destroy the concept of having a functional computer that you own and can run arbitrary stuff on.
Which, is why it's more important than ever to have a PC.
It, uh, was at least definitely possible to do a <$1000 computer back in 2020-25. Ours is under $1000 (I think we started at $400 for a no-GPU build in 2020ish, then got a used RX 580 ($150) once the GPU craze died down and a slightly better CPU ($100), and have an RX 6600 now). Though now with the exploding RAM prices...
-- Frost
You can totally do that yeah!
We have our stuff set up so inbound VPS traffic (for HTTPS) comes in on port 4430, while LAN traffic is on 443. It's not done for firewall reasons, it's so we can pass the client's IP through with Nginx's proxy_protocol feature, but you could just make your local-only services not listen on 4430. Boom, done.
Fail2Ban on the VPS is probably good. On the home server, it might just lock out the VPS (since everything comes from there).
Anyway yeah, I've got a whole guide on this sort of setup! https://frost.brightfur.net/blog/selfhosting-with-a-bounce-vps-part-1/
-- Frost