I like thinking about this concept!
In reality, a lot of regular hunting rifles fit this role well but the GPR likes to tease rifle nuts with some nuance. Closest I have had was a Ruger GSR with a few mods.
When you list the components it doesn’t sound like anything unusual, but I think other than a general trend towards compactness, it’s the sum of the parts: the weight, balance, handling, pointability, sights etc. that define what we think of as a GPR. In factory form the GSR, Steyr Scout, Sako Black Bear, Ruger Guide Gun, Tikka battue come close for me. My ‘tangible’ attributes:
Stock: probably a good quality synthetic, but I am not opposed to wood. I like the idea a of simple and strong adjustable cheek piece to adapt to different sights options.
Barrel: about 20” is perfect. Definitely no shorter than 18” (unless suppressed), no longer than 22. Nothing unique here but profile will matter for a good balance. I think something around a magnum sporter profile is good, not a tank, but it doesn’t have to be an ultralight profile.
Action: I am not fussy here. I do like less than 90deg bolt lifts, and I like a mod70 style safety. Neither of those two are deal breaker requirements. I could quite happily do with a Tikka, Mod70, Howa, Ruger 77, Sako and others. Short action is preferable.
Magazine: I like a DBM that can also be loaded through the ejection port. Not many offer this – Sauer/ Mauser, Sako, CZ. I like the sound of the AW magazines over AICS for this reason. I have seen a video of a Ruger GSR that was adapted to use AW mags. I know AICS are a solid standardized option but I am not sure why people think they are so amazing, other than popularity and interchangeability. In a perfect world the DBM would have a true flush fit option for carrying, and also an option for extended mags.
Sights: I have tried a scout scope and it’s not for me. Other than freeing the space around the receiver I hated the concept in the field. It think its irrelevant with today’s LPVO’s and red dots. A compact variable or LPVO over the action is better for me. BUIS can be a flip up rear ghost ring or decent barrel mounted sights. They need to be robust, highly visible. They are for 100m and in use IMO. Might never need them but I think they are cool. Being able to switch to a red dot on the rifle mounts would be very cool too.
Calibre/chambering: Somewhere between .264” and .308”. Head stamp is not critical other than ideally it’s a common chambering with abundant ammo, brass, etc. Basically, I think to be a true GPR it needs to be able to send at least a 130gr bullet with an impact velocity of 2000fps at 300-350m. That’s well within the capability of most common cartridges on the 308, x57, or 06 case. .308 is the obvious candidate but 6.5CM, .260, 7mm-08, .308 would all be good enough. If it’s a long action I would be happy with most options on the 06 or x57 case. Bottom end would likely be around 6.5CM, top end no bigger than .30-06 or 8x57.