I would always recommend good old Debian for a mostly „it just works“ experience. You‘ll find debian packages for most if not all the things you mentioned. Alternatively you could go the steeper route and use an immutable OS like Fedora CoreOS or Fedora Silverblue for a more desktopy experience.
Hardware wise I‘ve been told the Intel NUC kits work wonders, or similarly specced boxes from Asia. You might get like 32GB RAM, a fairly recent CPU for <400€. Personally I‘m using a 12 year old Mac Mini until it dies, running debian.
What is an unofficial ChatGPT API supposed to be? One where you dont have to pay? I‘d hazard a guess that if that exists, it would just be a wrapper around someone elses API token, for which they are paying. Questions is whether they know about that usage…