I would upgrade from your current Mini, not just to prevent screen tearing, but equally so because the older base M1 chip is relatively limited when it comes to performance. An adapter wouldn't raise the fps or graphics settings and playing on medium and not even getting constant 60+fps on such an older game that doesn't even have crazy graphics is honestly just bad. But that's MacOS for you, it will struggle especially in 4k. In any case, I think your Mini is severely underpowered for a 4k screen.
Now which one to get, Mini or Studio. I checked benchmarks for you. Unrelated to those, I'd get the Studio over the Mini anyways because of the better cooling, and because it has 2 additional USB-C ports (not Thunderbolt capable on the M2 Max, limited to 10Gbps USB protocol). You mentioned that all your ports are in use, even though the M2 Pro Mini would double these, I think 4 isn't really that much either and I wouldn't like the visual mess that's connecting a USB hub to the Mini (I'd want that to sit on the desk and be visible).
Now for the benchmarks: In general the base M1 and M2 chips seem to be the only one that really struggle with gaming. M1 Max/Ultra and M2 Pro/Max/Ultra are all noticeably faster and how close performance is depends on the game, resolution and graphics settings.
However, the M1 Max Studio struggles with older games in 4k, as a reference Shadow of the Tomb Raider runs with 30fps on higher settings, and Borderlands 3 on high settings is not playable. Since the M2 Max isn't a huge upgrade, more of an incremental one, this means graphics intense games still won't run well in 4k on the new M2 Max Studio. And Shadow.. uses an Apple Silicon native new version that is more efficient than many other games, yet it struggles in 4k regardless.
Civ VI specifically uses an older Intel port and does not have an ASi native version, likely never will. If Apple cuts Rosetta 2 from future MacOS releases, many years in the future, this means eventually you won't be able to launch the game anymore at all. But the more immediate effect is that it will never be able to really utilize the Apple Silicon to its full potential, no matter how many Ultras you throw at it. The hardware will just be more and more bored (idling).
The game being unoptimized means no matter how well it runs on a better chip, eventually, as you discover more of the map and the time to calculate turns increases, you will eventually end up with stuttering and slowdowns. There are games out there that are better optimized, apparently Total War: Warhammer III is one of those. Yet a M1/M2 Ultra won't be enough for 4k either (at least in the higher settings).
I found this graph in Luke Miani's latest Mac Studio review video on Youtube:
It shows there is a noticeable fps gain as you go from the M2 Pro to the M2 Max, but that is with an optimized game that can make better use of the ASi than Civ VI, and it's on lower settings. Sadly the M1 Max is missing here. This mainly just confirms that anything M2 Pro and up will have a noticeable performance increase over the M1/M2 base chips, but it doesn't really help to answer the question which Mac you should get.
I can't find any good info for what's better for Civ VI, M2 Pro or M2 Max. Notebookcheck has a database for game tests but they did not test in 4k and the rest of the tests are too few to say anything. gpucheck.com does not test Apple hardware at all. I do not know of any other resources that have Apple benchmarks. The Youtube ones were mostly useless as they just show performance in the early game parts.
Overall you'll certainly see slightly better fps on the Studio, there is a bit more CPU headroom too which should help with turn calculation times, maybe overall this even makes the difference between 4k gaming being ok vs. just a bit too stuttery. If you want the extra ports anyways, the Studio isn't much more expensive with the identical 32GiB RAM configuration.
As every little bit of extra performance will help improve the generally bad MacOS gaming performance, I think you should get the Studio. I'd expect the difference in average fps to be around 10-20fps. So if you get 40-50fps on the M2 Pro Mini, you'd get the better 60 on the Studio. But that's likely about it, the Studio certainly won't push 100fps, and the worst part is that if the Mini were to struggle with 30 fps on higher settings, then the Studio with an additional dozens fps or so won't make the difference either.
But that is something you'd really have to try for yourself, sadly there likely won't be a useful benchmark for you because how many people buy a M2 Max Studio, or M2 Pro Mini, or even both, and then play Civ VI on a 4k display? All these variables would have to come together exactly like that to get meaningful results.
If a couple more fps is worth the price difference to you, then the Studio absolutely will be better for you. If you expect a 50% performance uplift, it's unlikely to have that.
